Description |
1 online resource (xviii, 289-433 pages) |
Series |
Applied and numerical harmonic analysis |
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Applied and numerical harmonic analysis.
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Contents |
Part I. Traditional Methods for Computing Heat Kernels -- Introduction -- Stochastic Analysis Method -- A Brief Introduction to Calculus of Variations -- The Path Integral Approach -- The Geometric Method -- Commuting Operators -- Fourier Transform Method -- The Eigenfunctions Expansion Method -- Part II. Heat Kernel on Nilpotent Lie Groups and Nilmanifolds -- Laplacians and Sub-Laplacians -- Heat Kernels for Laplacians and Step 2 Sub-Laplacians -- Heat Kernel for Sub-Laplacian on the Sphere Ŝ3 -- Part III. Laguerre Calculus and Fourier Method -- Finding Heat Kernels by Using Laguerre Calculus -- Constructing Heat Kernel for Degenerate Elliptic Operators -- Heat Kernel for the Kohn Laplacian on the Heisenberg Group -- Part IV. Pseudo-Differential Operators -- The Psuedo-Differential Operators Technique -- Bibliography -- Index |
Summary |
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. The work is divided into four main parts: Part I treats the heat kernel by traditional methods, such as the Fourier transform method, paths integrals, variational calculus, and eigenvalue expansion; Part II deals with the heat kernel on nilpotent Lie groups and nilmanifolds; Part III examines Laguerre calculus applications; Part IV uses the method of pseudo-differential operators to describe heat kernels. Topics and features: •comprehensive treatment from the point of view of distinct branches of mathematics, such as stochastic processes, differential geometry, special functions, quantum mechanics, and PDEs; •novelty of the work is in the diverse methods used to compute heat kernels for elliptic and sub-elliptic operators; •most of the heat kernels computable by means of elementary functions are covered in the work; •self-contained material on stochastic processes and variational methods is included. 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 |
Analysis |
wiskunde |
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mathematics |
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fysica |
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physics |
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stochastische processen |
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stochastic processes |
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partial differential equations |
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toegepaste wiskunde |
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applied mathematics |
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differentiaalmeetkunde |
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differential geometry |
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waarschijnlijkheidstheorie |
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probability theory |
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Mathematics (General) |
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Wiskunde (algemeen) |
Bibliography |
Includes bibliographical references and index |
Notes |
Print version record |
Subject |
Elliptic operators.
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Fourier transformations.
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Transformaciones de Fourier
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Elliptic operators
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Fourier transformations
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Form |
Electronic book
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Author |
Calin, Ovidiu.
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ISBN |
9780817649951 |
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0817649956 |
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