Verfügbarkeit: Pseudo-differential equations and stochastics over non-Archimedean fields

Pseudo-differential equations and stochastics over non-Archimedean fields:

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1. Verfasser:	Kočubej, Anatolij Naumovyč 1949- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York [u.a.] Dekker 2001
Schriftenreihe:	Pure and applied mathematics 244
Schlagworte:	Mathematische Physik Stochastic analysis Stochastic partial differential equations Differential equations, Partial Mathematical physics Stochastische partielle Differentialgleichung Pseudodifferentialgleichung
Online-Zugang:	Publisher description Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references (p. 303-313) and index
Beschreibung:	XI, 316 S. 24 cm
ISBN:	0824706552

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MARC


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Datensatz im Suchindex

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adam_text	PSEUDO-DIFFERENTIAL EQUATIONS AND STOCHASTICS OVER NON-ARCHIMEDEAN FIELDS ANATOLY N. KOCHUBEI UKRAINIAN NATIONAL ACADEMY OF SCIENCES KIEV, UKRAINE MARCEL DEKKER, INC. NEW YORK * BASEL CONTENTS PREFACE III 1 PRELIMINARIES 1 1.1 FIELD EXTENSIONS 1 1.2 FINITE FIELDS 3 1.3 LOCAL FIELDS 5 1.4 POLYNOMIALS AND QUADRATIC FORMS 11 1.5 INTEGRATION AND HARMONIC ANALYSIS 14 1.6 DISTRIBUTIONS 17 1.7 HOMOGENEOUS DISTRIBUTIONS 21 1.8 GAUSSIAN INTEGRALS 24 1.9 ADELES 31 2 FUNDAMENTAL SOLUTIONS 35 2.1 THE RIESZ KERNEL 35 2.2 THE FRACTIONAL DIFFERENTIATION OPERATOR 38 2.3 THE FAMILY {D A ,A 0} AS A SEMIGROUP OF OPERATORS . . . . 41 2.4 THE FRACTIONAL DIFFERENTIAL OPERATOR ON IDELES AND ZEROES OF RIEMANN'S ZETA FUNCTION 46 2.5 PSEUDO-DIFFERENTIAL OPERATORS OVER A LOCAL FIELD 49 2.6 COORDINATE REPRESENTATION 57 2.7 FUNDAMENTAL SOLUTIONS OF ELLIPTIC OPERATORS 61 2.8 GREEN FUNCTIONS OF ELLIPTIC OPERATORS 72 2.9 HYPERBOLIC EQUATIONS 75 2.10 CAUCHY PROBLEM FOR AN EQUATION OF THE SCHRODINGER TYPE . . 78 2.11 ON SOME MODELS OF P-NDIC QUANTUM THEORY 88 2.12 COMMENTS 90 CONTENTS SPECTRAL THEORY 91 3.1 FRACTIONAL DIFFERENTIATION OPERATOR 91 3.2 "AN OPERATOR OF THE SCHRODINGER TYPE 94 3.3 SPECTRAL PROPERTIES OF D A ON OPEN SUBSETS OF A LOCAL FIELD . . 106 3.4 AN ANALOGUE OF THE HAMILTONIAN OF POINT INTERACTIONS . . . . 120 3.5 MULTIPLICATIVE FRACTIONAL DIFFERENTIATION 128 3.6 COMMENTS 130 PARABOLIC EQUATIONS 133 4.1 AN ANALOGUE OF THE HEAT EQUATION 133 4.2 PROBABILISTIC INTERPRETATION 143 4.3 STABILIZATION 146 4.4 GENERAL UNIQUENESS THEOREM 150 4.5 FUNDAMENTAL SOLUTIONS OF PARABOLIC EQUATIONS 152 4.6 HEAT EQUATION ON A BALL 162 4.7 HEAT EQUATION ON THE GROUP OF UNITS 167 4.8 ON PARABOLIC PSEUDO-DIFFERENTIAL EQUATIONS OVER R N 170 4.9 COMMENTS 191 CONSTRUCTION OF PROCESSES . 193 5.1 NOTATIONS AND PRELIMINARIES 193 5.2 STOCHASTIC INTEGRALS OF DETERMINISTIC FUNCTIONS 195 5.3 STOCHASTIC INTEGRALS OF RANDOM FUNCTIONS 202 5.4 STOCHASTIC DIFFERENTIAL EQUATIONS 205 5.5 ROTATION-INVARIANT PROCESSES WITH INDEPENDENT INCREMENTS . 212 5.6 THE GENERATOR AND ITS SPECTRUM 218 5.7 RECURRENCE AND HITTING PROBABILITIES 223 5.8 PROCESSES ON ADELES 228 5.9 GENERAL STABLE DISTRIBUTIONS 231 5.10 COMMENTS 242 ANALYSIS OVER INFINITE EXTENSIONS OF A LOCAL FIELD 245 6.1 MEASURABLE VECTOR SPACES 245 6.2 AN INFINITE EXTENSION AS A TOPOLOGICAL VECTOR SPACE 258 6.3 MEASURE AND INTEGRATION 260 6.4 FOURIER TRANSFORM AND FRACTIONAL DIFFERENTIATION 267 6.5 SPECTRUM 274 6.6 HEAT EQUATION 276 CONTENTS XI 6.7 HYPERSINGULAR INTEGRAL REPRESENTATION 282 6.8 COMMENTS 286 7 PROCESSES WITH NON-ARCHIMEDEAN TIME PARAMETERS 287 7.1 LOCAL FIELD BROWNIAN MOTION 287 7.2 THE WIENER PROCESS WITH THE P-ADIC TIME PARAMETER . . . . 293 7.3 COMMENTS 302 BIBLIOGRAPHY 303 INDEX 315
adam_txt	PSEUDO-DIFFERENTIAL EQUATIONS AND STOCHASTICS OVER NON-ARCHIMEDEAN FIELDS ANATOLY N. KOCHUBEI UKRAINIAN NATIONAL ACADEMY OF SCIENCES KIEV, UKRAINE MARCEL DEKKER, INC. NEW YORK * BASEL CONTENTS PREFACE III 1 PRELIMINARIES 1 1.1 FIELD EXTENSIONS 1 1.2 FINITE FIELDS 3 1.3 LOCAL FIELDS 5 1.4 POLYNOMIALS AND QUADRATIC FORMS 11 1.5 INTEGRATION AND HARMONIC ANALYSIS 14 1.6 DISTRIBUTIONS 17 1.7 HOMOGENEOUS DISTRIBUTIONS 21 1.8 GAUSSIAN INTEGRALS 24 1.9 ADELES 31 2 FUNDAMENTAL SOLUTIONS 35 2.1 THE RIESZ KERNEL 35 2.2 THE FRACTIONAL DIFFERENTIATION OPERATOR 38 2.3 THE FAMILY {D A ,A 0} AS A SEMIGROUP OF OPERATORS . . . . 41 2.4 THE FRACTIONAL DIFFERENTIAL OPERATOR ON IDELES AND ZEROES OF RIEMANN'S ZETA FUNCTION 46 2.5 PSEUDO-DIFFERENTIAL OPERATORS OVER A LOCAL FIELD 49 2.6 COORDINATE REPRESENTATION 57 2.7 FUNDAMENTAL SOLUTIONS OF ELLIPTIC OPERATORS 61 2.8 GREEN FUNCTIONS OF ELLIPTIC OPERATORS 72 2.9 HYPERBOLIC EQUATIONS 75 2.10 CAUCHY PROBLEM FOR AN EQUATION OF THE SCHRODINGER TYPE . . 78 2.11 ON SOME MODELS OF P-NDIC QUANTUM THEORY 88 2.12 COMMENTS 90 CONTENTS SPECTRAL THEORY 91 3.1 FRACTIONAL DIFFERENTIATION OPERATOR 91 3.2 "AN OPERATOR OF THE SCHRODINGER TYPE 94 3.3 SPECTRAL PROPERTIES OF D A ON OPEN SUBSETS OF A LOCAL FIELD . . 106 3.4 AN ANALOGUE OF THE HAMILTONIAN OF POINT INTERACTIONS . . . . 120 3.5 MULTIPLICATIVE FRACTIONAL DIFFERENTIATION 128 3.6 COMMENTS 130 PARABOLIC EQUATIONS 133 4.1 AN ANALOGUE OF THE HEAT EQUATION 133 4.2 PROBABILISTIC INTERPRETATION 143 4.3 STABILIZATION 146 4.4 GENERAL UNIQUENESS THEOREM 150 4.5 FUNDAMENTAL SOLUTIONS OF PARABOLIC EQUATIONS 152 4.6 HEAT EQUATION ON A BALL 162 4.7 HEAT EQUATION ON THE GROUP OF UNITS 167 4.8 ON PARABOLIC PSEUDO-DIFFERENTIAL EQUATIONS OVER R N 170 4.9 COMMENTS 191 CONSTRUCTION OF PROCESSES . 193 5.1 NOTATIONS AND PRELIMINARIES 193 5.2 STOCHASTIC INTEGRALS OF DETERMINISTIC FUNCTIONS 195 5.3 STOCHASTIC INTEGRALS OF RANDOM FUNCTIONS 202 5.4 STOCHASTIC DIFFERENTIAL EQUATIONS 205 5.5 ROTATION-INVARIANT PROCESSES WITH INDEPENDENT INCREMENTS . 212 5.6 THE GENERATOR AND ITS SPECTRUM 218 5.7 RECURRENCE AND HITTING PROBABILITIES 223 5.8 PROCESSES ON ADELES 228 5.9 GENERAL STABLE DISTRIBUTIONS 231 5.10 COMMENTS 242 ANALYSIS OVER INFINITE EXTENSIONS OF A LOCAL FIELD 245 6.1 MEASURABLE VECTOR SPACES 245 6.2 AN INFINITE EXTENSION AS A TOPOLOGICAL VECTOR SPACE 258 6.3 MEASURE AND INTEGRATION 260 6.4 FOURIER TRANSFORM AND FRACTIONAL DIFFERENTIATION 267 6.5 SPECTRUM 274 6.6 HEAT EQUATION 276 CONTENTS XI 6.7 HYPERSINGULAR INTEGRAL REPRESENTATION 282 6.8 COMMENTS 286 7 PROCESSES WITH NON-ARCHIMEDEAN TIME PARAMETERS 287 7.1 LOCAL FIELD BROWNIAN MOTION 287 7.2 THE WIENER PROCESS WITH THE P-ADIC TIME PARAMETER . . . . 293 7.3 COMMENTS 302 BIBLIOGRAPHY 303 INDEX 315
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author	Kočubej, Anatolij Naumovyč 1949-
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spelling	Kočubej, Anatolij Naumovyč 1949- Verfasser (DE-588)133201651 aut Pseudo-differential equations and stochastics over non-Archimedean fields Anatoly N. Kochubei New York [u.a.] Dekker 2001 XI, 316 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 244 Includes bibliographical references (p. 303-313) and index Mathematische Physik Stochastic analysis Stochastic partial differential equations Differential equations, Partial Mathematical physics Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Pseudodifferentialgleichung (DE-588)4121533-3 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s Pseudodifferentialgleichung (DE-588)4121533-3 s DE-604 Pure and applied mathematics 244 (DE-604)BV000001885 244 http://www.loc.gov/catdir/enhancements/fy0647/2001277692-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016412084&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kočubej, Anatolij Naumovyč 1949- Pseudo-differential equations and stochastics over non-Archimedean fields Pure and applied mathematics Mathematische Physik Stochastic analysis Stochastic partial differential equations Differential equations, Partial Mathematical physics Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Pseudodifferentialgleichung (DE-588)4121533-3 gnd
subject_GND	(DE-588)4135969-0 (DE-588)4121533-3
title	Pseudo-differential equations and stochastics over non-Archimedean fields
title_auth	Pseudo-differential equations and stochastics over non-Archimedean fields
title_exact_search	Pseudo-differential equations and stochastics over non-Archimedean fields
title_exact_search_txtP	Pseudo-differential equations and stochastics over non-Archimedean fields
title_full	Pseudo-differential equations and stochastics over non-Archimedean fields Anatoly N. Kochubei
title_fullStr	Pseudo-differential equations and stochastics over non-Archimedean fields Anatoly N. Kochubei
title_full_unstemmed	Pseudo-differential equations and stochastics over non-Archimedean fields Anatoly N. Kochubei
title_short	Pseudo-differential equations and stochastics over non-Archimedean fields
title_sort	pseudo differential equations and stochastics over non archimedean fields
topic	Mathematische Physik Stochastic analysis Stochastic partial differential equations Differential equations, Partial Mathematical physics Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Pseudodifferentialgleichung (DE-588)4121533-3 gnd
topic_facet	Mathematische Physik Stochastic analysis Stochastic partial differential equations Differential equations, Partial Mathematical physics Stochastische partielle Differentialgleichung Pseudodifferentialgleichung
url	http://www.loc.gov/catdir/enhancements/fy0647/2001277692-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016412084&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000001885
work_keys_str_mv	AT kocubejanatolijnaumovyc pseudodifferentialequationsandstochasticsovernonarchimedeanfields

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