Pseudo-differential equations and stochastics over non-Archimedean fields:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
2001
|
| Series: | Pure and applied mathematics
244 |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 303-313) and index |
| Physical Description: | XI, 316 S. 24 cm |
| ISBN: | 0824706552 |
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Record in the Search Index
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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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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:18:02Z |
| indexdate | 2024-08-03T00:35:41Z |
| institution | BVB |
| isbn | 0824706552 |
| language | English |
| lccn | 2001277692 |
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| physical | XI, 316 S. 24 cm |
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| publisher | Dekker |
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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 |