Direct And Inverse Finite Dimensional Spectral Problems On Graphs

Author : Manfred Möller,Vyacheslav Pivovarchik
Publisher : Springer Nature
Page : 349 pages
File Size : 46,9 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030604844

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Direct and Inverse Finite-Dimensional Spectral Problems on Graphs by Manfred Möller,Vyacheslav Pivovarchik Pdf

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.

Author : Pavel Kurasov
Publisher : Springer Nature
Page : 644 pages
File Size : 46,6 Mb
Release : 2023-12-09
Category : Science
ISBN : 9783662678725

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Spectral Geometry of Graphs by Pavel Kurasov Pdf

This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph. The book has two central themes: the trace formula and inverse problems. The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book. To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions. The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 49,7 Mb
Release : 2009-06-04
Category : Mathematics
ISBN : 9783764389628

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Combinatorial Number Theory and Additive Group Theory by Alfred Geroldinger,Imre Ruzsa Pdf

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Author : Pierluigi Contucci,Cristian Giardinà
Publisher : Cambridge University Press
Page : 383 pages
File Size : 49,8 Mb
Release : 2016-12-15
Category : Science
ISBN : 9781107124103

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Advances in Disordered Systems, Random Processes and Some Applications by Pierluigi Contucci,Cristian Giardinà Pdf

This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.

Author : Alston Scott Householder
Publisher : Unknown
Page : 552 pages
File Size : 48,8 Mb
Release : 1972
Category : Algebra
ISBN : STANFORD:36105033326336

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KWIC Index for Numerical Algebra by Alston Scott Householder Pdf

Author : Vladislav V. Kravchenko
Publisher : Springer Nature
Page : 155 pages
File Size : 53,7 Mb
Release : 2020-07-28
Category : Mathematics
ISBN : 9783030478490

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Direct and Inverse Sturm-Liouville Problems by Vladislav V. Kravchenko Pdf

This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Author : Steven Lord,Fedor Sukochev,Dmitriy Zanin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 416 pages
File Size : 47,9 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783110378054

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Theory by Steven Lord,Fedor Sukochev,Dmitriy Zanin Pdf

This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Author : Andries E. Brouwer,H. Van Maldeghem
Publisher : Unknown
Page : 481 pages
File Size : 45,5 Mb
Release : 2022-01-13
Category : Language Arts & Disciplines
ISBN : 9781316512036

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Strongly Regular Graphs by Andries E. Brouwer,H. Van Maldeghem Pdf

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

Author : V. A. Yurko
Publisher : Unknown
Page : 316 pages
File Size : 55,8 Mb
Release : 2002
Category : Inverse problems (Differential equations)
ISBN : 3110631210

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Method of Spectral Mappings in the Inverse Problem Theory by V. A. Yurko Pdf

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.

Author : Anonim
Publisher : Unknown
Page : 702 pages
File Size : 55,5 Mb
Release : 1995
Category : Aeronautics
ISBN : UIUC:30112048646605

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Scientific and Technical Aerospace Reports by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 866 pages
File Size : 46,8 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015082440879

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Mathematical Reviews by Anonim Pdf

Author : Mikhail S. Agranovich
Publisher : Springer
Page : 331 pages
File Size : 55,7 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9783319146485

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Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by Mikhail S. Agranovich Pdf

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
Page : 1626 pages
File Size : 44,8 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9780387929194

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Handbook of Mathematical Methods in Imaging by Otmar Scherzer Pdf

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Author : Ulf Grenander,Michael I. Miller,Michael Miller
Publisher : Oxford University Press
Page : 633 pages
File Size : 49,6 Mb
Release : 2007
Category : Computers
ISBN : 9780198505709

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Pattern Theory by Ulf Grenander,Michael I. Miller,Michael Miller Pdf

'Pattern Theory' provides a comprehensice & accessible overview of the modern challenges in signal, data & pattern analysis in speech recognition, computational linguistics, image analysis & computer vision. Aimed at graduate students the text includes numerous exercises & an extensive bibliography.

Author : Jussi Behrndt,Karl-Heinz Förster,Carsten Trunk
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 48,7 Mb
Release : 2010-01-11
Category : Mathematics
ISBN : 9783034601801

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Recent Advances in Operator Theory in Hilbert and Krein Spaces by Jussi Behrndt,Karl-Heinz Förster,Carsten Trunk Pdf

The present book is a memorial volume devoted to Peter Jonas. It displays recent advances in modern operator theory in Hilbert and Krein spaces and contains a collection of original research papers written by many well-known specialists in this field. The papers contain new results for problems close to the area of research of Peter Jonas: Spectral and perturbation problems for operators in inner product spaces, generalized Nevanlinna functions and definitizable functions, scattering theory, extension theory for symmetric operators, fixed points, hyperbolic matrix polynomials, moment problems, indefinite spectral and Sturm-Liouville problems, and invariant subspace problems. This book is written for researchers and postgraduates interested in functional analysis and differential operators.