Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications
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Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications
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Author : Manfred Möller
language : en
Publisher:
Release Date : 2015
Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications written by Manfred Möller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications
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Author : Manfred Möller
language : en
Publisher: Birkhäuser
Release Date : 2015-06-11
Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications written by Manfred Möller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-11 with Mathematics categories.
The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-λI for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader’s background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed.
Direct And Inverse Finite Dimensional Spectral Problems On Graphs
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Author : Manfred Möller
language : en
Publisher: Springer Nature
Release Date : 2020-10-30
Direct And Inverse Finite Dimensional Spectral Problems On Graphs written by Manfred Möller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Mathematics categories.
Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research.
Ukrainski Matematicheski Zhurnal
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Author :
language : uk
Publisher:
Release Date : 2007
Ukrainski Matematicheski Zhurnal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Advances In Shannon S Sampling Theory
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Author : Ahmed I. Zayed
language : en
Publisher: CRC Press
Release Date : 1993-07-23
Advances In Shannon S Sampling Theory written by Ahmed I. Zayed and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-23 with Mathematics categories.
Advances in Shannon's Sampling Theory provides an up-to-date discussion of sampling theory, emphasizing the interaction between sampling theory and other branches of mathematical analysis, including the theory of boundary-value problems, frames, wavelets, multiresolution analysis, special functions, and functional analysis. The author not only traces the history and development of the theory, but also presents original research and results that have never before appeared in book form. Recent techniques covered include the Feichtinger-Gröchenig sampling theory; frames, wavelets, multiresolution analysis and sampling; boundary-value problems and sampling theorems; and special functions and sampling theorems. The book will interest graduate students and professionals in electrical engineering, communications, and applied mathematics.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2000
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Analytic Theory Of Polynomials
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Author : Qazi Ibadur Rahman
language : en
Publisher: Oxford University Press
Release Date : 2002
Analytic Theory Of Polynomials written by Qazi Ibadur Rahman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Language Arts & Disciplines categories.
Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications
Distribution Of Zeros Of Entire Functions
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Author : Boris I͡Akovlevich Levin
language : en
Publisher: American Mathematical Soc.
Release Date : 1980-01-01
Distribution Of Zeros Of Entire Functions written by Boris I͡Akovlevich Levin 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 1980-01-01 with Mathematics categories.
Combinatorial Problems And Exercises
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Author : László Lovász
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Combinatorial Problems And Exercises written by László Lovász 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 2007 with Mathematics categories.
The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allows the reader to practice theechniques by completing the proof. In the third part, a full solution is provided for each problem. This book will be useful to those students who intend to start research in graph theory, combinatorics or their applications, and for those researchers who feel that combinatorial techniques mightelp them with their work in other branches of mathematics, computer science, management science, electrical engineering and so on. For background, only the elements of linear algebra, group theory, probability and calculus are needed.
Introduction To The Spectral Theory Of Polynomial Operator Pencils
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Author : A. S. Markus
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-09-14
Introduction To The Spectral Theory Of Polynomial Operator Pencils written by A. S. Markus 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 2012-09-14 with Education categories.
This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.