Denseness, Bases and Frames in Banach Spaces and Applications PDF Download

Author: Aref Jeribi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110493861
Category : Mathematics
Languages : en
Pages : 421

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Book Description
This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Author: Aref Jeribi
Publisher: Springer Nature
ISBN: 981162528X
Category : Mathematics
Languages : en
Pages : 509

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Book Description
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.

Author: Aref Jeribi
Publisher: CRC Press
ISBN: 135104625X
Category : Mathematics
Languages : en
Pages : 208

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Book Description
Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.

Author: Aymen Ammar
Publisher: CRC Press
ISBN: 1000293130
Category : Mathematics
Languages : en
Pages : 284

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Book Description
The concept of multivalued linear operators—or linear relations—is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators. The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations. The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

Author: Christopher Heil
Publisher: Springer Science & Business Media
ISBN: 0817646876
Category : Mathematics
Languages : en
Pages : 537

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Book Description
This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.

Author: Aref Jeribi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110596903
Category : Mathematics
Languages : en
Pages : 256

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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 1461206030
Category : Mathematics
Languages : en
Pages : 613

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Book Description
Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Author: Ole Christensen
Publisher: Birkhäuser
ISBN: 3319256130
Category : Mathematics
Languages : en
Pages : 704

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Book Description
This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005

Author: Jean Bourgain
Publisher: American Mathematical Soc.
ISBN: 082182323X
Category : Banach spaces
Languages : en
Pages : 111

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Book Description

Author: Michael Th. Rassias
Publisher: Springer Nature
ISBN: 3030618870
Category : Mathematics
Languages : en
Pages : 362

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Book Description
This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied. Contributions cover a variety of different topics and problems treated such as structure and optimization in computational harmonic analysis, sampling and approximation in shift invariant subspaces of L2(R), optimal rank one matrix decomposition, the Riemann Hypothesis, large sets avoiding rough patterns, Hardy Littlewood series, Navier–Stokes equations, sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools, harmonic functions in slabs and half-spaces, Andoni –Krauthgamer –Razenshteyn characterization of sketchable norms fails for sketchable metrics, random matrix theory, multiplicative completion of redundant systems in Hilbert and Banach function spaces. Efforts have been made to ensure that the content of the book constitutes a valuable resource for graduate students as well as senior researchers working on Harmonic Analysis and its various interconnections with related areas.