Semi-bounded Differential Operators, Contractive Semigroups and Beyond
Semi-bounded Differential Operators, Contractive Semigroups and Beyond

Author: Alberto Cialdea

Publisher: Springer

Published: 2014-07-21

Total Pages: 262

ISBN-13: 331904558X

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In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L2-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.

Harmonic Analysis and Partial Differential Equations
Harmonic Analysis and Partial Differential Equations

Author: Anatoly Golberg

Publisher: Springer Nature

Published: 2023-04-26

Total Pages: 319

ISBN-13: 3031254244

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Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Semi-bounded Differential Operators, Contractive Semigroups and Beyond
Semi-bounded Differential Operators, Contractive Semigroups and Beyond

Author: Alberto Cialdea

Publisher: Birkhäuser

Published: 2014-08-01

Total Pages: 252

ISBN-13: 9783319045573

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​In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L2-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.

Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial
Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial

Author: Peter Kuchment

Publisher: American Mathematical Soc.

Published: 2019-07-22

Total Pages: 322

ISBN-13: 147043783X

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This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.

Analysis
Analysis

Author: Jean-Paul Penot

Publisher: Springer

Published: 2016-12-18

Total Pages: 687

ISBN-13: 331932411X

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This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.

Multivariable Operator Theory
Multivariable Operator Theory

Author: Ernst Albrecht

Publisher: Springer Nature

Published: 2024-01-22

Total Pages: 893

ISBN-13: 3031505352

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Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations
Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations

Author: Sabir Umarov

Publisher: World Scientific

Published: 2018-02-13

Total Pages: 192

ISBN-13: 9813230991

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The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.

Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions
Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions

Author: Niels Jacob

Publisher: World Scientific

Published: 2020-01-22

Total Pages: 854

ISBN-13: 9811215510

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The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.

The Functional Calculus for Sectorial Operators
The Functional Calculus for Sectorial Operators

Author: Markus Haase

Publisher: Springer Science & Business Media

Published: 2006-08-18

Total Pages: 399

ISBN-13: 3764376988

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This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.