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

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Applied and Numerical Harmonic Analysis | SpringerLink BücherPublisher: Boston : Springer Science+Business Media, LLC, 2011Edition: 1Description: Online-Ressource (XVIII, 436p. 25 illus, digital)ISBN:
  • 9780817649951
Subject(s): Additional physical formats: 9780817649944 | Buchausg. u.d.T.: Heat kernels for elliptic and sub-elliptic operators. 1. ed. Cambridge, Mass. [u.a.] : Birkhäuser, 2011. XVIII, 433 S.DDC classification:
  • 515.353
MSC: MSC: *35-02 | 35Kxx | 35H10 | 47B34 | 81Q10 | 35A08 | 35R03RVK: RVK: SK 620LOC classification:
  • QA370-380
  • QA329.42
DOI: DOI: 10.1007/978-0-8176-4995-1Online resources: Summary: 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 S^3 -- 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.PPN: PPN: 1650434774Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
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