Download or read book Invariant Subspaces and Allied Topics written by Bhuri Singh Yadav and published by . This book was released on 1990 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Subspaces written by Heydar Radjavi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self-adjoint of the results have been obtained in operators on Hilbert space. Some the context of certain general studies: the theory of the characteristic operator function, initiated by Livsic; the study of triangular models by Brodskii and co-workers; and the unitary dilation theory of Sz. Nagy and Foia!? Other theorems have proofs and interest independent of any particular structure theory. Since the leading workers in each of the structure theories have written excellent expositions of their work, (cf. Sz.-Nagy-Foia!? [1], Brodskii [1], and Gohberg-Krein [1], [2]), in this book we have concentrated on results independent of these theories. We hope that we have given a reasonably complete survey of such results and suggest that readers consult the above references for additional information. The table of contents indicates the material covered. We have restricted ourselves to operators on separable Hilbert space, in spite of the fact that most of the theorems are valid in all Hilbert spaces and many hold in Banach spaces as well. We felt that this restriction was sensible since it eases the exposition and since the separable-Hilbert space case of each of the theorems is generally the most interesting and potentially the most useful case.
Download or read book Topics in the theory of invariant subspaces written by Demetrios Koros and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory of Dynamical Systems written by Mahendra Nadkarni and published by Springer Nature. This book was released on 2020-08-29 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein’s family of mixing rank-one automorphisms is given with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are also examined. Baire category theorems of ergodic theory, scattered in literature, are discussed in a unified way in the book. Riesz products are introduced and applied to describe the spectral types and eigenvalues of rank-one automorphisms. Lastly, the second edition includes a new chapter “Calculus of Generalized Riesz Products”, which discusses the recent work connecting generalized Riesz products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory and flat polynomials.
Download or read book Classification and Orbit Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2000 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence.
Download or read book Interpolation Spaces and Allied Topics in Analysis written by M. Cwikel and published by Springer. This book was released on 2006-12-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Measures and Dynamics Typical Behaviors written by Moacir Aloisio and published by Springer Nature. This book was released on 2023-10-27 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors. A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years. A valuable example of such subtleties is found in the so-called “Wonderland theorem” first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic). Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research. Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.
Download or read book Composition Operators on Function Spaces written by R.K. Singh and published by Elsevier. This book was released on 1993-11-03 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics. After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.
Download or read book Permanence of Invariant Subspaces Under Functional Calculus and Related Topics written by Gabriel Titu Prǎjiturǎ and published by . This book was released on 1999 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Isometries in Banach Spaces written by Richard J. Fleming and published by CRC Press. This book was released on 2007-11-15 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up where the first volume left off, the book begins with a chapter on the Banach-Stone property.
Download or read book Topological Dynamics and Applications written by Robert Ellis and published by American Mathematical Soc.. This book was released on 1998 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.
Download or read book Stability of Operators and Operator Semigroups written by Tanja Eisner and published by Birkhäuser. This book was released on 2019-10-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic behaviour, in particular "stability" in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.
Download or read book Accessions List South Asia written by Library of Congress. Library of Congress Office, New Delhi and published by . This book was released on 1990-08 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Operator Theory Systems and Networks written by Dym and published by Birkhäuser. This book was released on 2013-11-22 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on app1ications of linear operator theory to systems and networks, which was held at the Weizmann Institute of Science in the third week of June, 19S3, just be fore the MTNS Conference in Beersheva. For a 10ng time these subjects were studied indepen dent1y by mathematica1 ana1ysts and e1ectrica1 engineers. Never the1ess, in spite of the lack of communication, these two groups often deve10ped parallel theories, though in different languages, at different levels of genera1ity and typica11y quite different motivations. In the last severa1 years each side has become aware of the work of the other and there is a seeming1y ever increasing invo1vement of the abstract theories of factorization, extension and interpolation of operators (and operator/matrix va1ued functions) to the design and analysis of systems and net works. Moreover, the problems encountered in e1ectrica1 engineering have genera ted new mathematica1 problems, new approaches, and usefu1 new formu1ations. The papers contained in this volume constitute a more than representative se1ection of the presented talks and dis cussion at the workshop, and hopefu11y will also serve to give a reasonably accurate picture of the problems which are under active study today and the techniques which are used to deal with them."
Download or read book Invariant Subspaces and Other Topics written by Grigore Arsene and published by . This book was released on 1982-11 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Invariant Subspaces written by Henry Helson and published by . This book was released on 1964 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological Algebras Their Applications and Related Topics written by Krzysztof Jarosz and published by . This book was released on 2005 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
