Denseness Bases And Frames In Banach Spaces And Applications
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Denseness Bases And Frames In Banach Spaces And Applications
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Author : Aref Jeribi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19
Denseness Bases And Frames In Banach Spaces And Applications written by Aref Jeribi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
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
Problems In Finite Element Methods
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2024-11-01
Problems In Finite Element Methods written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
This book discusses major topics and problems in finite element methods. It is targeted to graduate students and researchers in applied mathematics, physics, and engineering, wishing to learn and familiarize themselves with finite element theory. The book describes the nodal method for squares or rectangles and triangles, as well as an increase of the error between exact solution and approximate solution. It discusses an approximation of positive symmetric first-order systems in the Friedrichs sense by finite element methods. In addition, the book also explains the continuous and discontinuous approximation methods, adapted to the structure of the transport equation, leading to linear systems of quasi-explicit resolution, and therefore commonly used in practice.
Perturbation Theory For Linear Operators
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2021-07-28
Perturbation Theory For Linear Operators written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-28 with Mathematics categories.
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.
Topological Fixed Point Theory In Suitable Banach Algebras With Applications
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
Topological Fixed Point Theory In Suitable Banach Algebras With Applications written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
This book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs. Its scope extends to a broad range of equations, encompassing nonlinear biological models as well as two-dimensional boundary value problems associated with burgeoning cell populations and functional systems of differential and integral inclusions. The book systematically introduces the principles of topological fixed-point theory, offering insights into various classes of both single-valued and multi-valued maps. The overarching goal is to disseminate key techniques and outcomes derived from fixed-point theory, with a specific emphasis on its application to both single-valued and multi-valued mappings within the framework of Banach algebras.
Linear Operators And Their Essential Pseudospectra
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Author : Aref Jeribi
language : en
Publisher: CRC Press
Release Date : 2018-04-17
Linear Operators And Their Essential Pseudospectra written by Aref Jeribi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-17 with Mathematics categories.
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.
Probabilistic And Stochastic Methods In Analysis With Applications
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Author : J.S. Byrnes
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-06-30
Probabilistic And Stochastic Methods In Analysis With Applications written by J.S. Byrnes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-30 with Mathematics categories.
Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.
Affine Density In Wavelet Analysis
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Author : Gitta Kutyniok
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-12
Affine Density In Wavelet Analysis written by Gitta Kutyniok and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Mathematics categories.
This volume provides a thorough and comprehensive treatment of irregular wavelet frames. It introduces and employs a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Coverage includes non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
Spectral Theory Of Multivalued Linear Operators
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Author : Aymen Ammar
language : en
Publisher: CRC Press
Release Date : 2021-09-14
Spectral Theory Of Multivalued Linear Operators written by Aymen Ammar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-14 with Mathematics categories.
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.
Harmonic Analysis And Applications
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Author : Christopher Heil
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-02
Harmonic Analysis And Applications written by Christopher Heil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-02 with Mathematics categories.
This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.
Operator Theory Operator Algebras And Applications
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Author : Deguang Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Operator Theory Operator Algebras And Applications written by Deguang Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.