Heat Kernels For Elliptic And Sub Elliptic Operators

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Heat Kernels for Elliptic and Sub-elliptic Operators

Author : Ovidiu Calin
Publisher : Springer Science & Business Media
ISBN 13 : 0817649956
Total Pages : 444 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Heat Kernels for Elliptic and Sub-elliptic Operators by : Ovidiu Calin

Download or read book Heat Kernels for Elliptic and Sub-elliptic Operators written by Ovidiu Calin and published by Springer Science & Business Media. This book was released on 2010-10-10 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : E. B. Davies
Publisher : Cambridge University Press
ISBN 13 : 9780521409971
Total Pages : 212 pages
Book Rating : 4.4/5 (99 download)

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Book Synopsis Heat Kernels and Spectral Theory by : E. B. Davies

Download or read book Heat Kernels and Spectral Theory written by E. B. Davies and published by Cambridge University Press. This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.

Heat Kernel Estimates for Elliptic Operators with Robin Boundary Conditions

Author : Chris Wong
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)

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Book Synopsis Heat Kernel Estimates for Elliptic Operators with Robin Boundary Conditions by : Chris Wong

Download or read book Heat Kernel Estimates for Elliptic Operators with Robin Boundary Conditions written by Chris Wong and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Heat Kernels and Dirac Operators

Author : Nicole Berline
Publisher : Springer Science & Business Media
ISBN 13 : 9783540200628
Total Pages : 384 pages
Book Rating : 4.2/5 (6 download)

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Book Synopsis Heat Kernels and Dirac Operators by : Nicole Berline

Download or read book Heat Kernels and Dirac Operators written by Nicole Berline and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

Author : Pascal Auscher
Publisher : American Mathematical Soc.
ISBN 13 : 0821833839
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by : Pascal Auscher

Download or read book Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces written by Pascal Auscher and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis, Geometry and Topology of Elliptic Operators

Author : Bernhelm Booss
Publisher : World Scientific
ISBN 13 : 9812773606
Total Pages : 553 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Analysis, Geometry and Topology of Elliptic Operators by : Bernhelm Booss

Download or read book Analysis, Geometry and Topology of Elliptic Operators written by Bernhelm Booss and published by World Scientific. This book was released on 2006 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gaussian Bounds for Reduced Heat Kernels of Subelliptic Operators on Nilpotent Lie Groups

Author : A. F. M. ter Elst
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (678 download)

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Book Synopsis Gaussian Bounds for Reduced Heat Kernels of Subelliptic Operators on Nilpotent Lie Groups by : A. F. M. ter Elst

Download or read book Gaussian Bounds for Reduced Heat Kernels of Subelliptic Operators on Nilpotent Lie Groups written by A. F. M. ter Elst and published by . This book was released on 1999 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Operators, Topology, and Asymptotic Methods

Author : John Roe
Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Elliptic Operators, Topology, and Asymptotic Methods by : John Roe

Download or read book Elliptic Operators, Topology, and Asymptotic Methods written by John Roe and published by Longman Scientific and Technical. This book was released on 1988 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities

Author : Marco Bramanti
Publisher : American Mathematical Soc.
ISBN 13 : 0821849034
Total Pages : 136 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities by : Marco Bramanti

Download or read book Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities written by Marco Bramanti and published by American Mathematical Soc.. This book was released on 2010 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: "March 2010, Volume 204, number 961 (end of volume)."

Heat Kernel and Analysis on Manifolds

Author : Alexander Grigoryan
Publisher : American Mathematical Soc.
ISBN 13 : 0821849352
Total Pages : 504 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Heat Kernel and Analysis on Manifolds by : Alexander Grigoryan

Download or read book Heat Kernel and Analysis on Manifolds written by Alexander Grigoryan and published by American Mathematical Soc.. This book was released on 2009 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Stochastic Geometric Analysis With Applications

Author : Ovidiu Calin
Publisher : World Scientific
ISBN 13 : 981128329X
Total Pages : 557 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Stochastic Geometric Analysis With Applications by : Ovidiu Calin

Download or read book Stochastic Geometric Analysis With Applications written by Ovidiu Calin and published by World Scientific. This book was released on 2023-11-21 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

Author : Edoardo Vescovi
Publisher : Springer
ISBN 13 : 3319634208
Total Pages : 246 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT by : Edoardo Vescovi

Download or read book Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT written by Edoardo Vescovi and published by Springer. This book was released on 2017-08-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis introduces readers to the type II superstring theories in the AdS5×S5 and AdS4×CP3 backgrounds. Each chapter exemplifies a different computational approach to measuring observables (conformal dimensions of single-trace operators and expectation values of Wilson loop operators) relevant for two supersymmetric theories: the N=4 super Yang-Mills theory and the N=6 Chern-Simons-matter (ABJM) theory. Perturbative techniques have traditionally been used to make quantitative predictions in quantum field theories, but they are only reliable as long as the interaction strengths are weak. The anti-de Sitter/conformal field theory (AdS/CFT) correspondence realizes physicists’ dream of studying strongly coupled quantum field theories with “enhanced” symmetries, using the methods provided by string theory. The first part of the thesis sets up the semiclassical quantization of worldsheet sigma-model actions around string solutions of least area in AdS space. This machinery is used to capture quantum corrections at large coupling to next-to-leading and next-to-next-to-leading order by solving the determinants of partial differential operators and by computing Feynman diagrams, respectively. In turn, the second part presents an innovative approach based on Monte Carlo simulations to finite coupling for a lattice-discretized model of the AdS5×S5 superstring action. The thesis focuses on fundamental aspects, as well as on applications previously published by the author, and offers a valuable reference work for anyone interested in the most recent developments in this field.

The Ubiquitous Heat Kernel

Author : Jay Jorgenson
Publisher : American Mathematical Soc.
ISBN 13 : 0821836986
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Ubiquitous Heat Kernel by : Jay Jorgenson

Download or read book The Ubiquitous Heat Kernel written by Jay Jorgenson and published by American Mathematical Soc.. This book was released on 2006 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

Author : Marco Bramanti
Publisher : Springer Science & Business Media
ISBN 13 : 3319020870
Total Pages : 157 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields by : Marco Bramanti

Download or read book An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields written by Marco Bramanti and published by Springer Science & Business Media. This book was released on 2013-11-20 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Long Time Estimates for the Heat Kernel Associated with a Uniformly Subellip[t]ic Symmetric Second Order Operator

Author : S. Kusuoka
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (162 download)

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Book Synopsis Long Time Estimates for the Heat Kernel Associated with a Uniformly Subellip[t]ic Symmetric Second Order Operator by : S. Kusuoka

Download or read book Long Time Estimates for the Heat Kernel Associated with a Uniformly Subellip[t]ic Symmetric Second Order Operator written by S. Kusuoka and published by . This book was released on 1986 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second order subelliptic operators have been the subject of a considerable amount of research in recent years. Starting with the paper Rothschild and Stein, in which the sharp form of Hormander's famous subellipticity theorem is proved, and continuing through the work of Fefferman and Phong and Sanchez-Calle, it has become increasingly clear that precise regularity estimates for these operators depend intimately on the geometry associated with the operator under consideration. The main purpose of this article is to obtain bounds, from above and below, on p(t, x, y), t epsilon (1, infinity), in terms of standard heat kernels.

Analysis and Mathematical Physics

Author : Björn Gustafsson
Publisher : Springer Science & Business Media
ISBN 13 : 3764399066
Total Pages : 513 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Analysis and Mathematical Physics by : Björn Gustafsson

Download or read book Analysis and Mathematical Physics written by Björn Gustafsson and published by Springer Science & Business Media. This book was released on 2009-10-02 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.

Partial Differential Equations and Mathematical Physics

Author : Kunihiko Kajitani
Publisher : Springer Science & Business Media
ISBN 13 : 9780817643096
Total Pages : 260 pages
Book Rating : 4.6/5 (43 download)

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Book Synopsis Partial Differential Equations and Mathematical Physics by : Kunihiko Kajitani

Download or read book Partial Differential Equations and Mathematical Physics written by Kunihiko Kajitani and published by Springer Science & Business Media. This book was released on 2002-12-13 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs---are presented in the areas of partial differential equations, complex analysis, and mathematical physics. Key subjects are: * Treated from the mathematical physics viewpoint: nonlinear stability of an expanding universe, the compressible Euler equation, spin groups and the Leray--Maslov index, * Linked to the Cauchy problem: an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy--Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem. Additional articles examine results on: * Local solvability for a system of partial differential operators, * The hypoellipticity of second order operators, * Differential forms and Hodge theory on analytic spaces, * Subelliptic operators and sub- Riemannian geometry. Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet- Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K. Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji, S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi The book is suitable as a reference text for graduate students and active researchers.