Spectral Theory Of Dynamical Systems

Author : Mahendra Nadkarni
Publisher : Springer Nature
Page : 223 pages
File Size : 43,6 Mb
Release : 2020-08-29
Category : Mathematics
ISBN : 9789811562259

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Spectral Theory of Dynamical Systems by Mahendra Nadkarni Pdf

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.

Author : Nadkarni
Publisher : Birkhäuser
Page : 182 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 3034888414

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Spectral Theory of Dynamical Systems by Nadkarni Pdf

This book treats some basic topics in the spectral theory of dynamical systems, where by a dynamical system we mean a measure space on which a group of automorphisms acts preserving the sets of measure zero. The treatment is at a general level, but even here, two theorems which are not on the surface, one due to H. Helson and W. Parry and the other due to B. Host are presented. Moreover non singular automorphisms are considered and systems ofimprimitivity are discussed. and they are used to describe Riesz products, suitably generalised, are considered the spectral types and eigenvalues of rank one automorphisms. On the other hand topics such as spectral characterisations of various mixing conditions, which can be found in most texts on ergodic theory, and also the spectral theory of Gauss Dynamical Systems, which is very well presented in Cornfeld, Fomin, and Sinai's book on Ergodic Theory, are not treated in this book. A number of discussions and correspondence on email with El Abdalaoui El Houcein made possible the presentation of mixing rank one construction of D. S. Ornstein. Iam deeply indebted to G. R. Goodson. He has edited the book and suggested a number of corrections and improvements in both content and language.

Author : Anonim
Publisher : Unknown
Page : 196 pages
File Size : 40,5 Mb
Release : 1998-03-01
Category : Electronic
ISBN : 3034888422

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Spectral Theory of Dynamical Systems by Anonim Pdf

Author : M. G. Nadkarni
Publisher : Unknown
Page : 216 pages
File Size : 45,8 Mb
Release : 1998
Category : Differentiable dynamical systems
ISBN : 8185931178

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Spectral Theory of Dynamical Systems by M. G. Nadkarni Pdf

Author : Martine Queffélec
Publisher : Springer
Page : 367 pages
File Size : 40,7 Mb
Release : 2010-01-30
Category : Mathematics
ISBN : 9783642112126

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Substitution Dynamical Systems - Spectral Analysis by Martine Queffélec Pdf

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.

Author : Martine Queffélec
Publisher : Springer
Page : 252 pages
File Size : 53,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540480884

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Substitution Dynamical Systems - Spectral Analysis by Martine Queffélec Pdf

Author : Martine Queffâelec
Publisher : Unknown
Page : 376 pages
File Size : 49,9 Mb
Release : 2010-09-10
Category : Differentiable dynamical systems
ISBN : 3642112552

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Substitution Dynamical Systems - Spectral Analysis by Martine Queffâelec Pdf

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.

Author : Christian Remling
Publisher : Walter de Gruyter GmbH & Co KG
Page : 264 pages
File Size : 55,8 Mb
Release : 2018-08-21
Category : Mathematics
ISBN : 9783110562286

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Spectral Theory of Canonical Systems by Christian Remling Pdf

Canonical systems occupy a central position in the spectral theory of second order differential operators. They may be used to realize arbitrary spectral data, and the classical operators such as Schrödinger, Jacobi, Dirac, and Sturm-Liouville equations can be written in this form. ‘Spectral Theory of Canonical Systems’ offers a selfcontained and detailed introduction to this theory. Techniques to construct self-adjoint realizations in suitable Hilbert spaces, a modern treatment of de Branges spaces, and direct and inverse spectral problems are discussed. Contents Basic definitions Symmetric and self-adjoint relations Spectral representation Transfer matrices and de Branges spaces Inverse spectral theory Some applications The absolutely continuous spectrum

Author : L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 49,9 Mb
Release : 2000-04-05
Category : Mathematics
ISBN : 3540663169

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Dynamical Systems, Ergodic Theory and Applications by L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik Pdf

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Author : Michel Weber
Publisher : European Mathematical Society
Page : 778 pages
File Size : 53,6 Mb
Release : 2009
Category : Mathematics
ISBN : 3037190469

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Dynamical Systems and Processes by Michel Weber Pdf

This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a great deal to the current research on almost-everywhere convergence problems. Researchers working in dynamical systems and at the crossroads of spectral theory, ergodic theory and stochastic processes will find the tools, methods, and results presented in this book of great interest. It is written in a style accessible to graduate students.

Author : David Eric Edmunds,W. D. Evans
Publisher : Oxford University Press
Page : 610 pages
File Size : 48,6 Mb
Release : 2018
Category : Mathematics
ISBN : 9780198812050

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Spectral Theory and Differential Operators by David Eric Edmunds,W. D. Evans Pdf

This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.--

Author : P.D. Hislop,I.M. Sigal
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461207412

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Introduction to Spectral Theory by P.D. Hislop,I.M. Sigal Pdf

The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.

Author : Ioannis Antoniou,Gunter Lumer
Publisher : CRC Press
Page : 360 pages
File Size : 54,7 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000657746

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Generalized Functions, Operator Theory, and Dynamical Systems by Ioannis Antoniou,Gunter Lumer Pdf

Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods.

Author : E. B. Davies
Publisher : Cambridge University Press
Page : 212 pages
File Size : 48,9 Mb
Release : 1989
Category : Mathematics
ISBN : 0521409977

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Heat Kernels and Spectral Theory by E. B. Davies Pdf

Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814479264

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Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology by Anonim Pdf