Holdings: The Lévy Laplacian

The Lévy Laplacian:

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Bibliographic Details
Main Author:	Feller, M. N. (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2005
Edition:	1. publ.
Series:	Cambridge tracts in mathematics 166
Subjects:	Dimension unendlich Laplace-Operator Partieller Differentialoperator
Online Access:	Inhaltsverzeichnis
Physical Description:	VI, 153 S.
ISBN:	0521846226 9780521846226

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MARC


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adam_text	THE LEVY LAPLACIAN M. N. FELLER CAMBRIDGE UNIVERSITY PRESS CONTENTS INTRODUCTION PAGE 1 1 THE LEVY LAPLACIAN 05 1.1 DEFINITION OF THE INFINITE-DIMENSIONAL LAPLACIAN 05 1.2 EXAMPLES OF LAPLACIANS FOR FUNCTIONS ON INFINITE- DIMENSIONAL SPACES 09 1.3 GAUSSIAN MEASURES 13 2 LEVY-LAPLACE OPERATORS 22 2.1 INFINITE-DIMENSIONAL ORTHOGONAL POLYNOMIALS 23 2.2 , THE SECOND-ORDER DIFFERENTIAL OPERATORS GENERATED BY THE LEVY LAPLACIAN 30 2.3 DIFFERENTIAL OPERATORS OF ARBITRARY ORDER GENERATED BY THE LEVY LAPLACIAN 33 3 SYMMETRIC LEVY-LAPLACE OPERATOR 40 3.1 THE SYMMETRIZED LEVY LAPLACIAN ON FUNCTIONS FROM THE DOMAIN OF DEFINITION OF THE LEVY-LAPLACE OPERATOR 40 3.2 THE LEVY LAPLACIAN ON FUNCTIONS FROM THE DOMAIN OF DEFINITION OF THE SYMMETRIZED LEVY-LAPLACE OPERATOR 44 3.3 SELF-ADJOINTNESS OF THE NON-SYMMETRIZED LEVY-LAPLACE OPERATOR 48 4 HARMONIC FUNCTIONS OF INFINITELY MANY VARIABLES 53 4.1 ARBITRARY SECOND-ORDER DERIVATIVES 54 4.2 ORTHOGONAL AND STOCHASTICALLY INDEPENDENT SECOND-ORDER DERIVATIVES 59 4.3 TRANSLATIONALLY NON-POSITIVE CASE 64 VI CONTENTS 5 LINEAR ELLIPTIC AND PARABOLIC EQUATIONS WITH LEVY LAPLACIANS 68 5.1 THE DIRICHLET PROBLEM FOR THE LEVY-LAPLACE AND LEVY-POISSON EQUATIONS 68 5.2 THE DIRICHLET PROBLEM FOR THE LEVY-SCHRODINGER STATIONARY EQUATION 84 5.3 THE RIQUIER PROBLEM FOR THE EQUATION WITH ITERATED LEVY LAPLACIANS 86 5.4 THE CAUCHY PROBLEM FOR THE HEAT EQUATION 88 6 QUASILINEAR AND NONLINEAR ELLIPTIC EQUATIONS WITH LEVY LAPLACIANS 92 6.1 THE DIRICHLET PROBLEM FOR THE EQUATION A L U(X) = F(U(X)) 92 6.2 THE DIRICHLET PROBLEM FOR THE EQUATION F(U(X), A L U(X)) = F{X) 94 6.3 THE RIQUIER PROBLEM FOR THE EQUATION A 2L U(X) = F(U(X)) 96 6.4 THE RIQUIER PROBLEM FOR THE EQUATION F(U(X),A 2L U(X)) = A L U(X) 99 6.5 THE RIQUIER PROBLEM FOR THE EQUATION F(U(X),A L U(X),A 2L U(X)) = 0 103 7 NONLINEAR PARABOLIC EQUATIONS WITH LEVY LAPLACIANS 108 7.1 THE CAUCHY PROBLEM FOR THE EQUATIONS DU(T, X)/DT = F(A L U(T, X)) AN D DU(T, X)/DT = F(T, A L U(T, X)) 108 7.2 THE CAUCHY PROBLEM FOR THE EQUATION DU(T, X)/DT = . F(U(T,X),A L U(T,X)) 115 7.3 THE CAUCHY PROBLEM FOR THE EQUATION = F{F(X),A L U{T,X)) 121 7.4 THE CAUCHY PROBLEM FOR THE EQUATION F(U(T, X), ; 8U(T,X)/DT, A L U(T,X)) = 0 126 APPENDIX. LEVY-DIRICHLET FORMS AND ASSOCIATED MARKOV PROCESSES 133 A. 1 THE DIRICHLET FORMS ASSOCIATED WITH THE LEVY-LAPLACE OPERATOR 133 A.2 THE STOCHASTIC PROCESSES ASSOCIATED WITH THE LEVY-DIRICHLET FORMS 137 BIBLIOGRAPHIC NOTES 142 REFERENCES 144 INDEX . 152
adam_txt	THE LEVY LAPLACIAN M. N. FELLER CAMBRIDGE UNIVERSITY PRESS CONTENTS INTRODUCTION PAGE 1 1 THE LEVY LAPLACIAN 05 1.1 DEFINITION OF THE INFINITE-DIMENSIONAL LAPLACIAN 05 1.2 EXAMPLES OF LAPLACIANS FOR FUNCTIONS ON INFINITE- DIMENSIONAL SPACES 09 1.3 GAUSSIAN MEASURES 13 2 LEVY-LAPLACE OPERATORS 22 2.1 INFINITE-DIMENSIONAL ORTHOGONAL POLYNOMIALS 23 2.2 , THE SECOND-ORDER DIFFERENTIAL OPERATORS GENERATED BY THE LEVY LAPLACIAN 30 2.3 DIFFERENTIAL OPERATORS OF ARBITRARY ORDER GENERATED BY THE LEVY LAPLACIAN 33 3 SYMMETRIC LEVY-LAPLACE OPERATOR 40 3.1 THE SYMMETRIZED LEVY LAPLACIAN ON FUNCTIONS FROM THE DOMAIN OF DEFINITION OF THE LEVY-LAPLACE OPERATOR 40 3.2 THE LEVY LAPLACIAN ON FUNCTIONS FROM THE DOMAIN OF DEFINITION OF THE SYMMETRIZED LEVY-LAPLACE OPERATOR 44 3.3 SELF-ADJOINTNESS OF THE NON-SYMMETRIZED LEVY-LAPLACE OPERATOR 48 4 HARMONIC FUNCTIONS OF INFINITELY MANY VARIABLES 53 4.1 ARBITRARY SECOND-ORDER DERIVATIVES 54 4.2 ORTHOGONAL AND STOCHASTICALLY INDEPENDENT SECOND-ORDER DERIVATIVES 59 4.3 TRANSLATIONALLY NON-POSITIVE CASE 64 VI CONTENTS 5 LINEAR ELLIPTIC AND PARABOLIC EQUATIONS WITH LEVY LAPLACIANS 68 5.1 THE DIRICHLET PROBLEM FOR THE LEVY-LAPLACE AND LEVY-POISSON EQUATIONS 68 5.2 THE DIRICHLET PROBLEM FOR THE LEVY-SCHRODINGER STATIONARY EQUATION 84 5.3 THE RIQUIER PROBLEM FOR THE EQUATION WITH ITERATED LEVY LAPLACIANS 86 5.4 THE CAUCHY PROBLEM FOR THE HEAT EQUATION 88 6 QUASILINEAR AND NONLINEAR ELLIPTIC EQUATIONS WITH LEVY LAPLACIANS 92 6.1 THE DIRICHLET PROBLEM FOR THE EQUATION A L U(X) = F(U(X)) 92 6.2 THE DIRICHLET PROBLEM FOR THE EQUATION F(U(X), A L U(X)) = F{X) 94 6.3 THE RIQUIER PROBLEM FOR THE EQUATION A 2L U(X) = F(U(X)) 96 6.4 THE RIQUIER PROBLEM FOR THE EQUATION F(U(X),A 2L U(X)) = A L U(X) 99 6.5 THE RIQUIER PROBLEM FOR THE EQUATION F(U(X),A L U(X),A 2L U(X)) = 0 103 7 NONLINEAR PARABOLIC EQUATIONS WITH LEVY LAPLACIANS 108 7.1 THE CAUCHY PROBLEM FOR THE EQUATIONS DU(T, X)/DT = F(A L U(T, X)) AN D DU(T, X)/DT = F(T, A L U(T, X)) 108 7.2 THE CAUCHY PROBLEM FOR THE EQUATION DU(T, X)/DT = . F(U(T,X),A L U(T,X)) 115 7.3 THE CAUCHY PROBLEM FOR THE EQUATION = F{F(X),A L U{T,X)) 121 7.4 THE CAUCHY PROBLEM FOR THE EQUATION F(U(T, X), ; 8U(T,X)/DT, A L U(T,X)) = 0 126 APPENDIX. LEVY-DIRICHLET FORMS AND ASSOCIATED MARKOV PROCESSES 133 A. 1 THE DIRICHLET FORMS ASSOCIATED WITH THE LEVY-LAPLACE OPERATOR 133 A.2 THE STOCHASTIC PROCESSES ASSOCIATED WITH THE LEVY-DIRICHLET FORMS 137 BIBLIOGRAPHIC NOTES 142 REFERENCES 144 INDEX . 152
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author	Feller, M. N.
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spelling	Feller, M. N. Verfasser aut The Lévy Laplacian M. N. Feller 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2005 VI, 153 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 166 Dimension unendlich swd Laplace-Operator swd Partieller Differentialoperator swd Cambridge tracts in mathematics 166 (DE-604)BV000000001 166 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014278457&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Feller, M. N. The Lévy Laplacian Cambridge tracts in mathematics Dimension unendlich swd Laplace-Operator swd Partieller Differentialoperator swd
title	The Lévy Laplacian
title_auth	The Lévy Laplacian
title_exact_search	The Lévy Laplacian
title_exact_search_txtP	The Lévy Laplacian
title_full	The Lévy Laplacian M. N. Feller
title_fullStr	The Lévy Laplacian M. N. Feller
title_full_unstemmed	The Lévy Laplacian M. N. Feller
title_short	The Lévy Laplacian
title_sort	the levy laplacian
topic	Dimension unendlich swd Laplace-Operator swd Partieller Differentialoperator swd
topic_facet	Dimension unendlich Laplace-Operator Partieller Differentialoperator
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014278457&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT fellermn thelevylaplacian

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