Heat Kernels for elliptic and sub-elliptic operators : methods and techniques
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 evol...
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| Auteurs principaux: | , , , |
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
Boston :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Serija: | Applied and Numerical Harmonic Analysis
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| Teme: | |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Description d'après consultation du 23 avril 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Heat kernels for elliptic and sub-elliptic operators, methods and techniques, Ovidiu Calin, Der-Chen Chang, Kenro Furutani... [et al.], [Basel], Birkhäuser, Springer, 2011, 1 vol. (XVIII-433 p.), Applied and numerical harmonic analysis, 978-0-8176-4994-4 |
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| 100 | 1 | |a Calin, Ovidiu, |d 19..-...., |c Mathématicien. | |
| 245 | 1 | 0 | |a Heat Kernels for elliptic and sub-elliptic operators : |b methods and techniques |c Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki. |
| 260 | |a Boston : |b Birkhäuser Boston. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Applied and Numerical Harmonic Analysis | |
| 500 | |a Description d'après consultation du 23 avril 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 425-429 Index p. 431-433 | ||
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Opérateurs elliptiques | ||
| 650 | |a Équation de la chaleur | ||
| 700 | 1 | |a Chang, Der-Chen Edward, |d 19..- |4 aut | |
| 700 | 1 | |a Furutani, Kenro, |d 19..- |4 aut | |
| 700 | 1 | |a Iwasaki, Chisato. |4 aut | |
| 776 | 0 | |0 148351611 |t Heat kernels for elliptic and sub-elliptic operators |o methods and techniques |f Ovidiu Calin, Der-Chen Chang, Kenro Furutani... [et al.] |c [Basel] |n Birkhäuser |n Springer |d 2011 |p 1 vol. (XVIII-433 p.) |s Applied and numerical harmonic analysis |z 978-0-8176-4994-4 | |
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| 997 | |0 967954 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||