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Geometric Harmonic Analysis I

A Sharp Divergence Theorem with Nontangential Pointwise Traces

de Dorina Mitrea, Irina Mitrea, Marius Mitrea ...

Series series Mathematics and Statistics (R0)
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for ... Leer más

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This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for
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Symplectic Difference Systems: Oscillation and Spectral Theory

de Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher ...

Series series Mathematics and Statistics (R0)
This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in ... Leer más

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This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in
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Introduction to Measure Theory and Functional Analysis

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Series series Mathematics and Statistics (R0)
This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two ... Leer más

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This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two
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Advances in Shannon's Sampling Theory

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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 ... Leer más

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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
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Functional Analytic Methods for Heat Green Operators

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Series series Mathematics and Statistics (R0)
This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl–Hörmander calculus of pseudo-differential operators to study heat Green operators through ... Leer más

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This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl–Hörmander calculus of pseudo-differential operators to study heat Green operators through
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Weakly Wandering Sequences in Ergodic Theory

de Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad ...

Series series Mathematics and Statistics (R0)
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Operators, Semigroups, Algebras and Function Theory

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Edición de Yemon Choi, Matthew Daws, Gordon Blower ...

Series series Springer Nature Proceedings excluding Computer Science
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Locally Convex Spaces

de M. Scott Osborne ...

Series series Mathematics and Statistics (R0)
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For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert
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Integral Equations on Time Scales

de Svetlin G. Georgiev ...

Series series Mathematics and Statistics (R0)
This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book ... Leer más

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This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book
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Operator Theory and Harmonic Analysis

OTHA 2020, Part II – Probability-Analytical Models, Methods and Applications

Edición de Alexey N. Karapetyants, Igor V. Pavlov, Albert N. Shiryaev ...

Series Libro 2 - Springer Nature Proceedings excluding Computer Science
This volume is part of the collaboration agreement between Springer and the ISAAC society.This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical ... Leer más

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The Analyst’s Gambit

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de Orr Moshe Shalit ...

The Analyst’s Gambit: A Second Course in Functional Analysis is a textbook written to serve a graduate course in Functional Analysis. It provides a sequel to the author’s previous volume, A First Course in Functional Analysis, but it is not necessary to have read one in order to make use of the other. As a graduate text, the reader is assumed to have taken undergraduate courses in set theory, ... Leer más

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The Analyst’s Gambit: A Second Course in Functional Analysis is a textbook written to serve a graduate course in Functional Analysis. It provides a sequel to the author’s previous volume, A First Course in Functional Analysis, but it is not necessary to have read one in order to make use of the other. As a graduate text, the reader is assumed to have taken undergraduate courses in set theory,
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Handbook of Analytic Operator Theory

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Series series CRC Press/Chapman and Hall Handbooks in Mathematics Series
Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators.The volume consists of eleven articles ... Leer más

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Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators.The volume consists of eleven articles
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Introductory Theory of Topological Vector SPates

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Series series Chapman & Hall/CRC Pure and Applied Mathematics
This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure ... Leer más

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Nonlinear Elliptic Partial Differential Equations

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Series series Mathematics and Statistics (R0)
This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite ... Leer más

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This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite
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Geometric Function Theory in Higher Dimension

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Series series Mathematics and Statistics (R0)
The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups ... Leer más

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The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups
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Principal Symbol Calculus on Contact Manifolds

de Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin ...

Series series Mathematics and Statistics (R0)
This book develops a C*-algebraic approach to the notion of principal symbol on Heisenberg groups and, using the fact that contact manifolds are locally modeled by Heisenberg groups, on compact contact manifolds. Applying abstract theorems due to Lord, Sukochev, Zanin and McDonald, a principal symbol on the Heisenberg group is introduced as a homomorphism of C*-algebras. This leads to a version of ... Leer más

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This book develops a C*-algebraic approach to the notion of principal symbol on Heisenberg groups and, using the fact that contact manifolds are locally modeled by Heisenberg groups, on compact contact manifolds. Applying abstract theorems due to Lord, Sukochev, Zanin and McDonald, a principal symbol on the Heisenberg group is introduced as a homomorphism of C*-algebras. This leads to a version of
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Variable Lebesgue Spaces

Foundations and Harmonic Analysis

de Alberto Fiorenza, David V. Cruz-Uribe ...

Series series Mathematics and Statistics (R0)
This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial ... Leer más

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This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial
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Achievements and Challenges in the Field of Convolution Operators

The Yuri Karlovich Anniversary Volume

Edición de Albrecht Böttcher, Oleksiy Karlovych, Eugene Shargorodsky, Ilya M. Spitkovsky ...

Series series Mathematics and Statistics (R0)
This volume, which is dedicated to Yuri Karlovich on the occasion of his 75th birthday, includes biographical material, personal reminiscences, and carefully selected papers.The contributions constituting the core of this volume are written by mathematicians who have collaborated with Yuri or have been influenced by his vast mathematical work. They are devoted to topics of Yuri Karlovich's work ... Leer más

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This volume, which is dedicated to Yuri Karlovich on the occasion of his 75th birthday, includes biographical material, personal reminiscences, and carefully selected papers.The contributions constituting the core of this volume are written by mathematicians who have collaborated with Yuri or have been influenced by his vast mathematical work. They are devoted to topics of Yuri Karlovich's work
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Generalized Multiresolution Analyses

de Kathy D. Merrill ...

Series series Mathematics and Statistics (R0)
This monograph presents the first unified exposition of generalized multiresolution analyses. Expanding on the author’s pioneering work in the field, these lecture notes provide the tools and framework for using GMRAs to extend results from classical wavelet analysis to a more general setting.Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension ... Leer más

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This monograph presents the first unified exposition of generalized multiresolution analyses. Expanding on the author’s pioneering work in the field, these lecture notes provide the tools and framework for using GMRAs to extend results from classical wavelet analysis to a more general setting.Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension
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Geometry in a Fréchet Context

A Projective Limit Approach

de C. T. J. Dodson, George Galanis, Efstathios Vassiliou ...

Series Libro 428 - London Mathematical Society Lecture Note Series
Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fréchet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Fréchet space, and the ... Leer más

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Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fréchet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Fréchet space, and the
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Analytic Methods in Number Theory

When Complex Numbers Count

de Wadim Zudilin ...

Series Libro 11 - Monographs in Number Theory
There is no surprise that arithmetic properties of integral ('whole') numbers are controlled by analytic functions of complex variable. At the same time, the values of analytic functions themselves happen to be interesting numbers, for which we often seek explicit expressions in terms of other 'better known' numbers or try to prove that no such exist. This natural symbiosis of number theory and ... Leer más

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There is no surprise that arithmetic properties of integral ('whole') numbers are controlled by analytic functions of complex variable. At the same time, the values of analytic functions themselves happen to be interesting numbers, for which we often seek explicit expressions in terms of other 'better known' numbers or try to prove that no such exist. This natural symbiosis of number theory and
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Convexity in Newton's Method

de José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón ...

Series series Mathematics and Statistics (R0)
This monograph examines a variety of iterative methods in Banach spaces with a focus on those obtained from the Newton method. Together with the authors’ previous two volumes on the topic of the Newton method in Banach spaces, this third volume significantly extends Kantorovich's initial theory. It accomplishes this by emphasizing the influence of the convexity of the function involved, showing ... Leer más

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This monograph examines a variety of iterative methods in Banach spaces with a focus on those obtained from the Newton method. Together with the authors’ previous two volumes on the topic of the Newton method in Banach spaces, this third volume significantly extends Kantorovich's initial theory. It accomplishes this by emphasizing the influence of the convexity of the function involved, showing
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Spectral Mapping Theorems

A Bluffer's Guide

de Robin Harte ...

Series series Mathematics and Statistics (R0)
Written by an author who was at the forefront of developments in multivariable spectral theory during the seventies and the eighties, this book describes the spectral mapping theorem in various settings. In this second edition, the Bluffer's Guide has been revised and expanded, whilst preserving the engaging style of the first.Starting with a summary of the basic algebraic systems – semigroups, ... Leer más

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Written by an author who was at the forefront of developments in multivariable spectral theory during the seventies and the eighties, this book describes the spectral mapping theorem in various settings. In this second edition, the Bluffer's Guide has been revised and expanded, whilst preserving the engaging style of the first.Starting with a summary of the basic algebraic systems – semigroups,
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Introduction to Measure Theory and Functional Analysis

Advances in Shannon's Sampling Theory

Functional Analytic Methods for Heat Green Operators

Weakly Wandering Sequences in Ergodic Theory

Operators, Semigroups, Algebras and Function Theory

Locally Convex Spaces

Integral Equations on Time Scales

Operator Theory and Harmonic Analysis

The Analyst’s Gambit

Handbook of Analytic Operator Theory

Introductory Theory of Topological Vector SPates

Nonlinear Elliptic Partial Differential Equations

Geometric Function Theory in Higher Dimension

Principal Symbol Calculus on Contact Manifolds

Variable Lebesgue Spaces

Achievements and Challenges in the Field of Convolution Operators

Generalized Multiresolution Analyses

Geometry in a Fréchet Context

Analytic Methods in Number Theory

Convexity in Newton's Method

Spectral Mapping Theorems