Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations

Author : Johannes Sjöstrand
Publisher : Springer
Page : 496 pages
File Size : 54,8 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9783030108199

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Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations by Johannes Sjöstrand Pdf

The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.

Author : Mats Andersson,Jan Boman,Christer Kiselman,Pavel Kurasov,Ragnar Sigurdsson
Publisher : Birkhäuser
Page : 466 pages
File Size : 42,8 Mb
Release : 2017-09-04
Category : Mathematics
ISBN : 9783319524719

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Analysis Meets Geometry by Mats Andersson,Jan Boman,Christer Kiselman,Pavel Kurasov,Ragnar Sigurdsson Pdf

This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.

Author : Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft
Publisher : Springer Nature
Page : 663 pages
File Size : 40,9 Mb
Release : 2022-10-03
Category : Mathematics
ISBN : 9783030875022

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Current Trends in Analysis, its Applications and Computation by Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft Pdf

This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.

Author : John Locker
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 44,9 Mb
Release : 2000
Category : Nonselfadjoint operators
ISBN : 9780821820490

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Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators by John Locker Pdf

Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Erik P. van den Ban,Johan A.C. Kolk
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 48,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9780817682446

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Geometric Aspects of Analysis and Mechanics by Erik P. van den Ban,Johan A.C. Kolk Pdf

Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields. Written in his honor, the invited and refereed articles in this volume contain important new results as well as surveys in some of these areas, clearly demonstrating the impact of Duistermaat's research and, in addition, exhibiting interrelationships among many of the topics.

Author : Sergio Albeverio,P. Kurasov
Publisher : Cambridge University Press
Page : 454 pages
File Size : 50,5 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 052177912X

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Singular Perturbations of Differential Operators by Sergio Albeverio,P. Kurasov Pdf

Differential (and more general self-adjoint) operators involving singular interactions arise naturally in a range of topics such as, classical and quantum physics, chemistry, and electronics. This book presents a systematic mathematical study of these operators, with particular emphasis on spectral and scattering problems. Suitable for researchers in analysis or mathematical physics, this book could also be used as a text for an advanced course on the applications of analysis.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,8 Mb
Release : 2024-06-11
Category : Electronic
ISBN : 9789814469111

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Further Progress in Analysis by Anonim Pdf

Author : A. Okay Celebi
Publisher : World Scientific
Page : 877 pages
File Size : 48,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812837332

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Further Progress in Analysis by A. Okay Celebi Pdf

The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.

Author : T. Aoki,H. Majima,Y. Takei,N. Tose
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 54,8 Mb
Release : 2009-03-15
Category : Mathematics
ISBN : 9784431732402

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Algebraic Analysis of Differential Equations by T. Aoki,H. Majima,Y. Takei,N. Tose Pdf

This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.

Author : Rafael del Río,Carlos Villegas-Blas
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 42,5 Mb
Release : 2004
Category : Schrödinger operator
ISBN : 9780821832974

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Spectral Theory of Schrodinger Operators by Rafael del Río,Carlos Villegas-Blas Pdf

This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.

Author : Ivan Veselic
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 46,5 Mb
Release : 2008-01-02
Category : Mathematics
ISBN : 9783540726890

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Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators by Ivan Veselic Pdf

This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.

Author : Aref Jeribi
Publisher : Springer Nature
Page : 509 pages
File Size : 50,6 Mb
Release : 2021-07-28
Category : Mathematics
ISBN : 9789811625282

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Perturbation Theory for Linear Operators by Aref Jeribi Pdf

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 : V.A. Il'in
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461517559

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Spectral Theory of Differential Operators by V.A. Il'in Pdf

In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term of a spectral function and its Riesz means without recourse to the traditional Carleman technique and Tauberian theorem apparatus.

Author : Anonim
Publisher : Unknown
Page : 974 pages
File Size : 53,9 Mb
Release : 2004
Category : Mathematics
ISBN : UOM:39015055144722

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Mathematical Reviews by Anonim Pdf

Author : Lloyd N. Trefethen,Mark Embree
Publisher : Princeton University Press
Page : 634 pages
File Size : 54,5 Mb
Release : 2005-08-07
Category : Mathematics
ISBN : 0691119465

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Spectra and Pseudospectra by Lloyd N. Trefethen,Mark Embree Pdf

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.