TY  - BOOK
AU  - Calin,Ovidiu
AU  - Chang,Der-Chen
AU  - Furutani,Kenro
AU  - Iwasaki,Chisato
ED  - SpringerLink (Online service)
TI  - Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques 
T2  - Applied and Numerical Harmonic Analysis
SN  - 9780817649951
AV  - QA370-380 
U1  - 515.353 23
PY  - 2011///
CY  - Boston
PB  - Birkhäuser Boston
KW  - Mathematics
KW  - Harmonic analysis
KW  - Operator theory
KW  - Differential equations, partial
KW  - Global differential geometry
KW  - Distribution (Probability theory)
KW  - Mathematical physics
KW  - Partial Differential Equations
KW  - Mathematical Methods in Physics
KW  - Operator Theory
KW  - Differential Geometry
KW  - Probability Theory and Stochastic Processes
KW  - Abstract Harmonic Analysis
N1  - 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
N2  - 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
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-8176-4995-1
ER  -