| Dewey Class |
515.353 (DDC 23) |
| Titolo |
Heat Kernels for Elliptic and Sub-elliptic Operators ([Ebook]) : Methods and Techniques / by Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki. |
| Autore |
Calin, Ovidiu |
| Added Personal Name |
Chang, Der-Chen |
| Furutani, Kenro |
| Iwasaki, Chisato |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1.st edition |
| Pubblicazione |
Boston : Birkhäuser , 2011. |
| Physical Details |
XVIII, 436 pages:. 25 illus. : online resource. |
| Serie |
Applied and numerical harmonic analysis |
| ISBN |
9780817649951 |
| Summary Note |
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: â¢comprehensive treatment from the point of view of distinct branches of mathematics, such as stochastic processes, differential geometry, special functions, quantum mechanics, and PDEs; â¢novelty of the work is in the diverse methods used to compute heat kernels for elliptic and sub-elliptic operators; â¢most of the heat kernels computable by means of elementary functions are covered in the work; â¢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.: |
| Contents note |
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. |
| System details note |
Online access is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-0-8176-4995-1 |
| Link alle Opere Legate |
Riferimenti soggetto: .
Abstract Harmonic Analysis .
Differential equations, Partial .
Differential Geometry .
Distribution (Probability theory) .
Global differential geometry .
Mathematical Methods in Physics .
Mathematical Physics .
Operator Theory .
Partial differential equations .
Probability theory and stochastic processes .
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