Download or read book Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations written by Damir Z. Arov and published by . This book was released on 2014-05-14 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essentially self-contained treatment ideal for mathematicians, physicists or engineers whose research is connected with inverse problems.
Download or read book Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2012-09-13 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essentially self-contained treatment ideal for mathematicians, physicists or engineers whose research is connected with inverse problems.
Download or read book Multivariate Prediction de Branges Spaces and Related Extension and Inverse Problems written by Damir Z. Arov and published by Birkhäuser. This book was released on 2018-05-30 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rational spectral densities. The underlying mathematics needed to tackle this class of problems is developed in careful detail, but, to ease the reading, an attempt is made to avoid excessive generality. En route a number of results that, to the best of our knowledge, were only known for p = 1 are generalized to the case p > 1.
Download or read book Indefinite Inner Product Spaces Schur Analysis and Differential Equations written by Daniel Alpay and published by Birkhäuser. This book was released on 2018-01-30 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer’s chief research interests and will appeal to a broad readership whose work involves operator theory.
Download or read book Inverse Problems for Fractional Partial Differential Equations written by Barbara Kaltenbacher and published by American Mathematical Society. This book was released on 2023-07-13 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters. The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case. The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.
Download or read book Linear State Signal Systems written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2022-05-26 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.
Download or read book Quaternionic de Branges Spaces and Characteristic Operator Function written by Daniel Alpay and published by Springer Nature. This book was released on 2020-01-27 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book.
Download or read book Probability Geometry and Integrable Systems written by Mark Pinsky and published by Cambridge University Press. This book was released on 2008-03-17 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.
Download or read book Inverse Problems in Partial Differential Equations written by David L. Colton and published by SIAM. This book was released on 1990-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Polynomial Equation Systems written by and published by Cambridge University Press. This book was released on with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Polynomial Equation Systems written by Teo Mora and published by Cambridge University Press. This book was released on 2003 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.
Download or read book Solving Polynomial Equation Systems IV Volume 4 Buchberger Theory and Beyond written by Teo Mora and published by Cambridge University Press. This book was released on 2016-04-01 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Download or read book Ultrametric Pseudodifferential Equations and Applications written by Andrei Yu. Khrennikov and published by Cambridge University Press. This book was released on 2018-04-26 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.
Download or read book Variational Methods for Nonlocal Fractional Problems written by Giovanni Molica Bisci and published by Cambridge University Press. This book was released on 2016-03-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.
Download or read book Solving Polynomial Equation Systems III Volume 3 Algebraic Solving written by Teo Mora and published by Cambridge University Press. This book was released on 2015-08-07 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Download or read book Operator Theory Function Spaces and Applications written by Tanja Eisner and published by Birkhäuser. This book was released on 2016-09-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of Damir Arov and to the sixty-fifth birthday of Leiba Rodman, both leading figures in the area of operator theory and its applications, in particular, to systems theory.
