Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques - Rilegato

Calin, Ovidiu; Chang, Der-Chen; Furutani, Kenro; Iwasaki, Chisato

Rilegato

ISBN 10: 0817649948 ISBN 13: 9780817649944

Casa editrice: Springer Basel AG, 2010

Riassunto

With each methodology treated in its own chapter, this monograph is a thorough exploration of several theories that can be used to find explicit formulas for heat kernels for both elliptic and sub-elliptic operators.

Su questo libro

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer Basel AG
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0817649948
• ISBN 13: 9780817649944
• Rilegatura: Copertina rigida
• Numero di pagine: 456
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