Heat Kernels For Elliptic And Sub Elliptic Operators

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Heat Kernels for Elliptic and Sub-elliptic Operators

Ovidiu Calin,Der-Chen Chang,Kenro Furutani,Chisato Iwasaki
Heat Kernels for Elliptic and Sub elliptic Operators Book PDF

Author : Ovidiu Calin,Der-Chen Chang,Kenro Furutani,Chisato Iwasaki
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 44,5 Mb
Release : 2010-10-10
Category : Mathematics
ISBN : 9780817649951

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Heat Kernels for Elliptic and Sub-elliptic Operators by Ovidiu Calin,Der-Chen Chang,Kenro Furutani,Chisato Iwasaki Pdf

This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Heat Kernels and Spectral Theory

E. B. Davies
Heat Kernels and Spectral Theory Book PDF

Author : E. B. Davies
Publisher : Cambridge University Press
Page : 212 pages
File Size : 51,6 Mb
Release : 1989
Category : Mathematics
ISBN : 0521409977

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Heat Kernels and Spectral Theory by E. B. Davies Pdf

Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.

Analysis and Partial Differential Equations: Perspectives from Developing Countries

Julio Delgado,Michael Ruzhansky
Analysis and Partial Differential Equations Perspectives from Developing Countries Book PDF

Author : Julio Delgado,Michael Ruzhansky
Publisher : Springer
Page : 269 pages
File Size : 50,8 Mb
Release : 2019-01-27
Category : Mathematics
ISBN : 9783030056575

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Analysis and Partial Differential Equations: Perspectives from Developing Countries by Julio Delgado,Michael Ruzhansky Pdf

This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries. Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China. Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.

Analysis, Geometry and Topology of Elliptic Operators

Bernhelm Booss,Krzysztof P. Wojciechowski
Analysis Geometry and Topology of Elliptic Operators Book PDF

Author : Bernhelm Booss,Krzysztof P. Wojciechowski
Publisher : World Scientific
Page : 553 pages
File Size : 50,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812773609

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Analysis, Geometry and Topology of Elliptic Operators by Bernhelm Booss,Krzysztof P. Wojciechowski Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.

The Sub-Laplacian Operators of Some Model Domains

Der-Chen Chang,Jingzhi Tie
The Sub Laplacian Operators of Some Model Domains Book PDF

Author : Der-Chen Chang,Jingzhi Tie
Publisher : Walter de Gruyter GmbH & Co KG
Page : 266 pages
File Size : 46,7 Mb
Release : 2022-08-01
Category : Mathematics
ISBN : 9783110642995

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The Sub-Laplacian Operators of Some Model Domains by Der-Chen Chang,Jingzhi Tie Pdf

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.

Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski

Matthias Lesch,Weiping Zhang,Slawomir Klimek,Bernhelm Booss-bavnbek
Analysis Geometry And Topology Of Elliptic Operators Papers In Honor Of Krzysztof P Wojciechowski Book PDF

Author : Matthias Lesch,Weiping Zhang,Slawomir Klimek,Bernhelm Booss-bavnbek
Publisher : World Scientific
Page : 553 pages
File Size : 46,8 Mb
Release : 2006-04-25
Category : Mathematics
ISBN : 9789814478021

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Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski by Matthias Lesch,Weiping Zhang,Slawomir Klimek,Bernhelm Booss-bavnbek Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.

Heat Kernel and Analysis on Manifolds

Alexander Grigoryan
Heat Kernel and Analysis on Manifolds Book PDF

Author : Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 504 pages
File Size : 53,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821849354

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Heat Kernel and Analysis on Manifolds by Alexander Grigoryan Pdf

"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré 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."--Publisher's website.

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

Marco Bramanti
An Invitation to Hypoelliptic Operators and H rmander s Vector Fields Book PDF

Author : Marco Bramanti
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 42,5 Mb
Release : 2013-11-20
Category : Mathematics
ISBN : 9783319020877

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An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields by Marco Bramanti Pdf

​Hörmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active field of research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development.

Heat Kernels and Dirac Operators

Nicole Berline,Ezra Getzler,Michèle Vergne
Heat Kernels and Dirac Operators Book PDF

Author : Nicole Berline,Ezra Getzler,Michèle Vergne
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 42,7 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540200622

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Heat Kernels and Dirac Operators by Nicole Berline,Ezra Getzler,Michèle Vergne Pdf

In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.

Heat Kernel Method and its Applications

Ivan Avramidi
Heat Kernel Method and its Applications Book PDF

Author : Ivan Avramidi
Publisher : Birkhäuser
Page : 390 pages
File Size : 41,7 Mb
Release : 2015-11-26
Category : Mathematics
ISBN : 9783319262666

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Heat Kernel Method and its Applications by Ivan Avramidi Pdf

The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.

Stochastic Geometric Analysis With Applications

Ovidiu Calin
Stochastic Geometric Analysis With Applications Book PDF

Author : Ovidiu Calin
Publisher : World Scientific
Page : 557 pages
File Size : 54,7 Mb
Release : 2023-11-21
Category : Mathematics
ISBN : 9789811283291

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Stochastic Geometric Analysis With Applications by Ovidiu Calin Pdf

This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.

Mathematical Physics, Spectral Theory and Stochastic Analysis

Michael Demuth,Werner Kirsch
Mathematical Physics Spectral Theory and Stochastic Analysis Book PDF

Author : Michael Demuth,Werner Kirsch
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 55,5 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9783034805919

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Mathematical Physics, Spectral Theory and Stochastic Analysis by Michael Demuth,Werner Kirsch Pdf

This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

Partial Differential Equations and Spectral Theory

Michael Demuth,Bert-Wolfgang Schulze,Ingo Witt
Partial Differential Equations and Spectral Theory Book PDF

Author : Michael Demuth,Bert-Wolfgang Schulze,Ingo Witt
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 54,9 Mb
Release : 2011-02-01
Category : Mathematics
ISBN : 9783034800242

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Partial Differential Equations and Spectral Theory by Michael Demuth,Bert-Wolfgang Schulze,Ingo Witt Pdf

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Neuromathematics of Vision

Giovanna Citti,Alessandro Sarti
Neuromathematics of Vision Book PDF

Author : Giovanna Citti,Alessandro Sarti
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 44,5 Mb
Release : 2014-02-08
Category : Mathematics
ISBN : 9783642344442

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Neuromathematics of Vision by Giovanna Citti,Alessandro Sarti Pdf

This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains: neurophysiology, phenomenology of perception and neurocognitive imaging. Imaging techniques like functional MRI and diffusion tensor MRI allow to deepen the study of cortical structures. Due to this variety of experimental data, neuromathematematics deals with modelling both cortical structures and perceptual spaces. From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in non commutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural morphologies and possibly of the emergence of perceptual units. But at the center of the neurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision. The contributions to this book come from the very founders of the discipline.

Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

Pascal Auscher,T. Coulhon,Alexander Grigoryan
Heat Kernels and Analysis on Manifolds Graphs and Metric Spaces Book PDF

Author : Pascal Auscher,T. Coulhon,Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 44,8 Mb
Release : 2003
Category : Elliptic operators
ISBN : 9780821833834

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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by Pascal Auscher,T. Coulhon,Alexander Grigoryan Pdf

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.