Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations

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Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Author : Johannes Sjöstrand
Publisher : Springer
ISBN 13 : 3030108198
Total Pages : 489 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations by : Johannes Sjöstrand

Download or read book Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations written by Johannes Sjöstrand and published by Springer. This book was released on 2019-05-17 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis Meets Geometry

Author : Mats Andersson
Publisher : Birkhäuser
ISBN 13 : 3319524712
Total Pages : 464 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Analysis Meets Geometry by : Mats Andersson

Download or read book Analysis Meets Geometry written by Mats Andersson and published by Birkhäuser. This book was released on 2017-09-04 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Current Trends in Analysis, its Applications and Computation

Author : Paula Cerejeiras
Publisher : Springer Nature
ISBN 13 : 3030875024
Total Pages : 663 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Current Trends in Analysis, its Applications and Computation by : Paula Cerejeiras

Download or read book Current Trends in Analysis, its Applications and Computation written by Paula Cerejeiras and published by Springer Nature. This book was released on 2022-10-03 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Aspects of Analysis and Mechanics

Author : Erik P. van den Ban
Publisher : Springer Science & Business Media
ISBN 13 : 0817682449
Total Pages : 401 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometric Aspects of Analysis and Mechanics by : Erik P. van den Ban

Download or read book Geometric Aspects of Analysis and Mechanics written by Erik P. van den Ban and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Further Progress in Analysis

Author : A. Okay Celebi
Publisher : World Scientific
ISBN 13 : 9812837337
Total Pages : 877 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Further Progress in Analysis by : A. Okay Celebi

Download or read book Further Progress in Analysis written by A. Okay Celebi and published by World Scientific. This book was released on 2009 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Further Progress In Analysis - Proceedings Of The 6th International Isaac Congress

Author : A Okay Celebi
Publisher : World Scientific
ISBN 13 : 9814469114
Total Pages : 877 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Further Progress In Analysis - Proceedings Of The 6th International Isaac Congress by : A Okay Celebi

Download or read book Further Progress In Analysis - Proceedings Of The 6th International Isaac Congress written by A Okay Celebi and published by World Scientific. This book was released on 2009-01-13 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Analysis of Differential Equations

Author : T. Aoki
Publisher : Springer Science & Business Media
ISBN 13 : 4431732403
Total Pages : 349 pages
Book Rating : 4.4/5 (317 download)

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Book Synopsis Algebraic Analysis of Differential Equations by : T. Aoki

Download or read book Algebraic Analysis of Differential Equations written by T. Aoki and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Fields Estimation

Author : Alexander G. Ramm
Publisher : World Scientific
ISBN 13 : 9812703152
Total Pages : 388 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Random Fields Estimation by : Alexander G. Ramm

Download or read book Random Fields Estimation written by Alexander G. Ramm and published by World Scientific. This book was released on 2005 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 974 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators

Author : Ivan Veselic
Publisher : Springer Science & Business Media
ISBN 13 : 3540726896
Total Pages : 151 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators by : Ivan Veselic

Download or read book Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators written by Ivan Veselic and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Results in Quantum Mechanics

Author : Jaroslav Dittrich
Publisher : Birkhäuser
ISBN 13 : 3034887450
Total Pages : 387 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Mathematical Results in Quantum Mechanics by : Jaroslav Dittrich

Download or read book Mathematical Results in Quantum Mechanics written by Jaroslav Dittrich and published by Birkhäuser. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schrödinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.

Operator Theory and Its Applications

Author : Michael Levitin
Publisher : American Mathematical Soc.
ISBN 13 : 0821852728
Total Pages : 192 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operator Theory and Its Applications by : Michael Levitin

Download or read book Operator Theory and Its Applications written by Michael Levitin and published by American Mathematical Soc.. This book was released on 2010 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the theory of linear operators in Hilbert spaces and its applications, the subjects covered in this book range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity.

Nuclear Science Abstracts

Author :
Publisher :
ISBN 13 :
Total Pages : 1132 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Nuclear Science Abstracts by :

Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 1132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis on Graphs and Its Applications

Author : Pavel Exner
Publisher : American Mathematical Soc.
ISBN 13 : 0821844717
Total Pages : 721 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analysis on Graphs and Its Applications by : Pavel Exner

Download or read book Analysis on Graphs and Its Applications written by Pavel Exner and published by American Mathematical Soc.. This book was released on 2008 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 722 pages
Book Rating : 4.:/5 (43 download)

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Book Synopsis Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews by :

Download or read book Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews written by and published by . This book was released on 1988 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectra and Pseudospectra

Author : Lloyd N. Trefethen
Publisher : Princeton University Press
ISBN 13 : 9780691119465
Total Pages : 634 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Spectra and Pseudospectra by : Lloyd N. Trefethen

Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2005-08-07 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Waveguides

Author : Pavel Exner
Publisher : Springer
ISBN 13 : 3319185764
Total Pages : 398 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Quantum Waveguides by : Pavel Exner

Download or read book Quantum Waveguides written by Pavel Exner and published by Springer. This book was released on 2015-05-31 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.