Author: Alexander Grigor'yan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110700859
Category : Mathematics
Languages : en
Pages : 556
Book Description
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Author: Alexander Grigor'yan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110700859
Category : Mathematics
Languages : en
Pages : 556
Book Description
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110700859
Category : Mathematics
Languages : en
Pages : 556
Book Description
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Author: Alexander Grigor'yan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311070076X
Category : Mathematics
Languages : en
Pages : 526
Book Description
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311070076X
Category : Mathematics
Languages : en
Pages : 526
Book Description
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
The Sub-Laplacian Operators of Some Model Domains
Author: Der-Chen Chang
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110642999
Category : Mathematics
Languages : en
Pages : 266
Book Description
The book studies sub-Laplacian operators on a family of model domains in C^{n+1}, which is a good point-wise model for a $CR$ manifold with non-degenerate Levi form. A considerable amount of study has been devoted to partial differential operators constructed from non-commuting vector fields, in which the non-commutativity plays an essential role in determining the regularity properties of the operators.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110642999
Category : Mathematics
Languages : en
Pages : 266
Book Description
The book studies sub-Laplacian operators on a family of model domains in C^{n+1}, which is a good point-wise model for a $CR$ manifold with non-degenerate Levi form. A considerable amount of study has been devoted to partial differential operators constructed from non-commuting vector fields, in which the non-commutativity plays an essential role in determining the regularity properties of the operators.
Real Hypersurfaces in Hermitian Symmetric Spaces
Author: Jürgen Berndt
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110689839
Category : Mathematics
Languages : en
Pages : 388
Book Description
Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classification results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110689839
Category : Mathematics
Languages : en
Pages : 388
Book Description
Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classification results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.
Heat Kernel and Analysis on Manifolds
Author: Alexander Grigoryan
Publisher: American Mathematical Soc.
ISBN: 0821893939
Category : Education
Languages : en
Pages : 504
Book Description
The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels. Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.Titles in this series are co-published with International Press, Cambridge, MA, USA.
Publisher: American Mathematical Soc.
ISBN: 0821893939
Category : Education
Languages : en
Pages : 504
Book Description
The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels. Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.Titles in this series are co-published with International Press, Cambridge, MA, USA.
Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
Author: Pascal Auscher
Publisher: American Mathematical Soc.
ISBN: 0821833839
Category : Mathematics
Languages : en
Pages : 434
Book Description
This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.
Publisher: American Mathematical Soc.
ISBN: 0821833839
Category : Mathematics
Languages : en
Pages : 434
Book Description
This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.
Potentials and Partial Differential Equations
Author: Suzanne Lenhart
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110792729
Category : Mathematics
Languages : en
Pages : 298
Book Description
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110792729
Category : Mathematics
Languages : en
Pages : 298
Book Description
From Classical Analysis to Analysis on Fractals
Author: Patricia Alonso Ruiz
Publisher: Springer Nature
ISBN: 3031378008
Category : Mathematics
Languages : en
Pages : 294
Book Description
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
Publisher: Springer Nature
ISBN: 3031378008
Category : Mathematics
Languages : en
Pages : 294
Book Description
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
Geometric Potential Analysis
Author: Mario Milman
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110741717
Category : Science
Languages : en
Pages : 370
Book Description
This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110741717
Category : Science
Languages : en
Pages : 370
Book Description
This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.
Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis
Author: Daniel Alpay
Publisher: Springer Nature
ISBN: 3031214609
Category : Mathematics
Languages : en
Pages : 424
Book Description
This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.
Publisher: Springer Nature
ISBN: 3031214609
Category : Mathematics
Languages : en
Pages : 424
Book Description
This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.