Download or read book Operator Extensions Interpolation of Functions and Related Topics written by A. Gheondea and published by Birkhäuser. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1976 the Institute of Mathematics of the Romanian Academy (formerly the Department of Mathematics of INCREST) and the Faculty of Mathematics (formerly the Faculty of Sciences) of the University ofTimi~oara have organized several Con ferences on Operator Theory. These Conferences were held yearly in Timi~oara (or in Timi~oara and Herculane) and beginning with 1985 they were held in Bucharest (1985,1986), in Timi~oara (1988) and in Predeal (1990). At the beginning, these Conferences answered the need of a part of the Romanian Mathematical Community ofexploring other forms of survival, after the dissolution of the Institute of Mathematics in 1975. Soon, these meetings evolved to International Conferences with a broad participation and where important results in Operator Theory and Operator Algebras and their interplay with Complex Function Theory, Differential Equations, Mathematical Physics, System Theory, etc. were presented. The 14th Conference on Operator Theory was held between June 1st and June 5th 1992, at the University ofTimi~oara. It was partially supported by the Institute of Mathematics of the Romanian Academy and by the Faculty of Mathematics of the University ofTimi~oara. Another important contribution towards covering the costs of this meeting came from The Soros Foundation for an Open Society. Without this generous help the organizing of this event would be impossible. Since 1980, the Proceedings of OT Conferences were published by Birkhauser Verlag in the series Operator Theory: Advances and Applications. The abstracts of the talks were collected in the Conference Report, published by the University of Timi~oara.

Download or read book Operator Extensions Interpolation of Functions and Related Topics written by Aurelian Gheondea and published by . This book was released on 1993 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1976 the Institute of Mathematics of the Romanian Academy (formerly the Department of Mathematics of INCREST) and the Faculty of Mathematics (formerly the Faculty of Sciences) of the University ofTimi~oara have organized several Con ferences on Operator Theory. These Conferences were held yearly in Timi~oara (or in Timi~oara and Herculane) and beginning with 1985 they were held in Bucharest (1985,1986), in Timi~oara (1988) and in Predeal (1990). At the beginning, these Conferences answered the need of a part of the Romanian Mathematical Community ofexploring other forms of survival, after the dissolution of the Institute of Mathematics in 1975. Soon, these meetings evolved to International Conferences with a broad participation and where important results in Operator Theory and Operator Algebras and their interplay with Complex Function Theory, Differential Equations, Mathematical Physics, System Theory, etc. were presented. The 14th Conference on Operator Theory was held between June 1st and June 5th 1992, at the University ofTimi~oara. It was partially supported by the Institute of Mathematics of the Romanian Academy and by the Faculty of Mathematics of the University ofTimi~oara. Another important contribution towards covering the costs of this meeting came from The Soros Foundation for an Open Society. Without this generous help the organizing of this event would be impossible. Since 1980, the Proceedings of OT Conferences were published by Birkhauser Verlag in the series Operator Theory: Advances and Applications. The abstracts of the talks were collected in the Conference Report, published by the University of Timi~oara.

Download or read book Topics in Interpolation Theory written by Bernd Fritzsche and published by Birkhäuser. This book was released on 2012-12-06 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: About one half of the papers in this volume are based on lectures which were pre sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. He would have been eighty years old. These have been supplemented by: (1) Historical material, based on reminiscences of former colleagues, students and associates of V.P. Potapov. (2) Translations of a number of important papers (which serve to clarify the Potapov approach to problems of interpolation and extension, as well as a number of related problems and methods) and are relatively unknown in the West. (3) Two expository papers, which have been especially written for this volume. For purposes of discussion, it is convenient to group the technical papers in this volume into six categories. We will now run through them lightly, first listing the major theme, then in parentheses the authors of the relevant papers, followed by discussion. Some supplementary references are listed at the end; OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications. It was dedicated to V.P. Potapov. 1. Multiplicative decompositions (Yu.P. Ginzburg; M.S. Livsic, I.V. Mikhailova; V.I. Smirnov).

Download or read book Topics In Interpolation Theory written by Harry Dym and published by Springer Science & Business Media. This book was released on 1997 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Petrovich Potapov, as remembered by colleagues, friends and former students.- On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc.- On tangential interpolation in reproducing kernel Hilbert modules and applications.- Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions.- The indefinite metric in the Schur interpolation problem for analytic functions, IV.- Bitangential interpolation for upper triangular operators.- Bitangential interpolation for upper triangular operators when the Pick operator is strictly positive.- Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class.- On recovering a multiplicative integral from its modulus.- On Schur functions and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J theory subject.- On transformations of Potapov's fundamental matrix inequality.- An abstract interpolation problem and the extension theory of isometric operators.- On the theory of matrix-valued functions belonging to the Smirnov class.- Integral representation of function of class Ka.- On the theory of entire matrix-functions of exponential type.- Analogs of Nehari and Sarason theorems for character-automorphic functions and some related questions.- The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner functions.- On a criterion of positive definiteness.- Matrix boundary value problems with eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh functions of the canonical periodical system of differential equations.- On boundary values of functions regular in a disk.

Download or read book Nonselfadjoint Operators and Related Topics written by A. Feintuch and published by Birkhäuser. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x- , (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, , y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model [NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later.

Download or read book Operator Theory System Theory and Related Topics written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the refereed proceedings of the Conference in Operator The ory in Honour of Moshe Livsic 80th Birthday, held June 29 to July 4, 1997, at the Ben-Gurion University of the Negev (Beer-Sheva, Israel) and at the Weizmann In stitute of Science (Rehovot, Israel). The volume contains papers in operator theory and its applications (understood in a very wide sense), many of them reflecting, 1 directly or indirectly, a profound impact of the work of Moshe Livsic. Moshe (Mikhail Samuilovich) Livsic was born on July 4, 1917, in the small town of Pokotilova near Uman, in the province of Kiev in the Ukraine; his family moved to Odessa when he was four years old. In 1933 he enrolled in the Department of Physics and Mathematics at the Odessa State University, where he became a student of M. G. Krein and an active participant in Krein's seminar - one of the centres where the ideas and methods of functional analysis and operator theory were being developed. Besides M. G. Krein, M. S. Livsic was strongly influenced B. Va. Levin, an outstanding specialist in the theory of analytic functions. A by deep understanding of operator theory as well as function theory and a penetrating search of connections between the two, were to become one of the landmarks of M. S. Livsic's work. M. S. Livsic defended his Ph. D.

Download or read book Interpolation Theory Systems Theory and Related Topics written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Download or read book J Contractive Matrix Valued Functions and Related Topics written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2008-11-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.

Download or read book Contributions to Operator Theory and Its Applications written by Takayuki Furuta and published by Springer Science & Business Media. This book was released on 1993 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Certain (Nearly) Convex Joint Numerical Ranges.- The Two-Sided Nevanlinna-Pick Problem in the Stieltjes Class.- State Space Formulas for Coprime Factorizations.- Generalization of Heinz-Kato Theorem via Furuta Inequality.- The Band Method for Bordered Algebras.- Lp-Distance Between Unitary Orbits in Type III? Factors.- Finite Dimensional Solution Sets of Extremal Problems in H1.- Factorization of Operators with Angularly Constrained Spectra.- On the Coefficients of Riemann Mappings on the Unit Disk into Itself.- Weak-Star Limits of Polynomials and their Derivatives.- Hausdorff Dimension of Some Fractals and Perron-Frobenius Theory.- Operators Which have Commutative Polar Decompositions.- Trace Formula for the Perturbation of Partial Differential Operator and Cyclic Cocycle on a Generalized Heisenberg Group.

Download or read book Operator Theory and Analysis written by H. Bart and published by Birkhäuser. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: On November 12-14, 1997 a workshop was held at the Vrije Universiteit Amsterdam on the occasion of the sixtieth birthday ofM. A. Kaashoek. The present volume contains the proceedings of this workshop. The workshop was attended by 44 participants from all over the world: partici pants came from Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, The Netherlands, South Africa, Switzerland, Ukraine and the USA. The atmosphere at the workshop was very warm and friendly. There where 21 plenary lectures, and each lecture was followed by a lively discussion. The workshop was supported by: the Vakgroep Wiskunde of the Vrije Univer siteit, the department of Mathematics and Computer Science of the Vrije Univer siteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics of the Erasmus University Rotterdam. The organizers would like to take this opportunity to express their gratitude for the support. Without it the workshop would not have been so successful as it was. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Photograph of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Curriculum Vitae of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Publications of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix l. Gohberg Opening Address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi H. Bart, A. C. M. Ran and H. I. Woerdeman Personal Reminiscences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv V. Adamyan and R. Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Conditions for the Separation of Spectral Components . . . . . . . 4 3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Download or read book Schur Functions Operator Colligations and Reproducing Kernel Pontryagin Spaces written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Download or read book Operator Theory and Boundary Eigenvalue Problems written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.

Download or read book Modern Analysis and Applications written by Vadim Adamyan and published by Springer Science & Business Media. This book was released on 2009-08-29 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

Download or read book Operator Methods in Ordinary and Partial Differential Equations written by Sergio Albeverio and published by Birkhäuser. This book was released on 2012-12-06 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: CO«i»b.H BaCHJIbeBHa lU>BaJIeBcR8JI (Sonja Kovalevsky) was born in Moscow in 1850 and died in Stockholm in 1891. Between these years, in the then changing and turbulent circumstances for Europe, lies the all too brief life of this remarkable woman. This life was lived out within the great European centers of power and learning in Russia, France, Germany, Switzerland, England and Sweden. To this day, now 150 years after her birth, her influence for and contribution to mathe matics, science, literature, women's rights and democratic government are recorded and reviewed, not only in Europe but now in countries far removed in time and distance from the lands of her birth and being. This volume, dedicated to her memory and to her achievements, records the Proceedings of the Marcus Wallenberg Symposium held, in memory of Sonja Kovalevsky, at Stockholm University from 18 to 22 June 2000. The symposium was held at the Department of Mathematics with its excellent library and lecture halls providing favourable working conditions. Within these pages are contained a curriculum vitae for Sonja Kovalevsky, a list of all her scientific publications, together with a copy of the moving and elegant obituary notice written by her friend and protector Gosta Mittag-Leffler. These papers are followed by a leading article entitled Sonja Kovalevsky: Her life and professorship in Stockholm, written especially for this volume by Jan-Erik Bjork in preparation for his major address to the Symposium.

Download or read book Toeplitz Operators and Related Topics written by Estelle L. Basor and published by Birkhäuser. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Harold Widom, a distinguished mathematician and renowned expert in the area of Toeplitz, Wiener-Hopf and pseudodifferential operators, on the occasion of his sixtieth birthday. The book opens with biographical material and a list of the mathematician's publications, this being followed by two papers based on Toeplitz lectures which he delivered at Tel Aviv University in March, 1993. The rest of the book consists of a selection of papers containing some recent achievements in the following areas: Szegö-Widom asymptotic formulas for determinants of finite sections of Toeplitz matrices and their generalizations, the Fisher-Hartwig conjecture, random matrices, analysis of kernels of Toeplitz matrices, projectional methods and eigenvalue distribution for Toeplitz matrices, the Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorff type theorems. The book will appeal to a wide audience of pure and applied mathematicians.

Download or read book New Aspects in Interpolation and Completion Theories written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of eight papers containing recent advances in interpolation theory for matrix functions and completion theory for matrices and operators. In the first paper, D. Alpay and P. Loubaton, "The tangential trigonometric moment problem on an interval and related topics" a trigonometric moment problem on an interval for matrix valued functions is studied. The realization approach plays an important role in solving this problem. The second paper, M. Bakonyi, V.G. Kaftal, G. Weiss and H.J. Woerdeman, "Max imum entropy and joint norm bounds for operator extensions" is dedicated to a matrix completion problem. In it is considered the problem when only the lower triangular part of the operator entries of a matrix is identified. Completions which have simultaneously a small usual norm and a small Hilbert-Schmidt norm are considered. Bounds for these norms are obtained. The analysis of the maximum entropy extension plays a special role. The paper contains applications to nest algebras and integral operators. The third paper, J .A. Ball, I. Gohberg and M.A. Kaashoek, "Bitangential interpola tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems. The main attention is focused on the time varying analog of the Nevanlinna-Pick tangential problem in the case where the inter polation conditions appear from two sides. The state space theory of time varying systems play an important role.

Download or read book Matrix and Operator Valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers on different aspects of operator theory and complex analysis, covering the recent achievements of the Odessa-Kharkov school, where Potapov was very active. The book appeals to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.