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Superanalysis:

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Bibliographic Details
Main Author:	Khrennikov, Andrei 1958- (Author)
Format:	Book
Language:	English
Published:	Dordrecht [u.a.] Kluwer Acad. Publ. 1999
Series:	Mathematics and its applications 470
Subjects:	Analysis Superraum
Online Access:	Inhaltsverzeichnis
Item Description:	Aus dem Russ. übers.
Physical Description:	IX, 347 S.
ISBN:	0792356071

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MARC


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Record in the Search Index

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adam_text	SUPERANALYSIS BY ANDREI KHRENNIKOV DEPARTMENT OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCES, UNIVERSITY OFVAEXJOE, VAEXJOE, SWEDEN AND DEPARTMENT OF MATHEMATICS, MOSCOW STATE UNIVERSITY OF ELECTRONIC ENGINEERING, ZELENOGRAD, MOSCOW, RUSSIA # KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON TABLE OF CONTENTS INTRODUCTION 1 I ANALYSIS ON A SUPERSPACE OVER BANACH SUPERALGE- BRAS 7 1. DIFFERENTIAL CALCULUS 7 2. CAUCHY-RIEMANN CONDITIONS AND THE CONDITION OF *- LINEARITY OF DERIVATIVES 21 3. INTEGRAL CALCULUS 26 4. INTEGRATION OF DIFFERENTIAL FORMS OF COMMUTING VARI ABLES 43 5. REVIEW OF THE DEVELOPMENT OF SUPERANALYSIS 51 6. UNSOLVED PROBLEMS AND POSSIBLE GENERALIZATIONS ... 56 II GENERALIZED FUNCTIONS ON A SUPERSPACE 57 1. LOCALLY CONVEX SUPERALGEBRAS AND SUPERMODULES . . 60 2. ANALYTIC GENERALIZED FUNCTIONS ON THE VLADIMIROV-VO- LOVICH SUPERSPACE 63 3. FOURIER TRANSFORMATION OF SUPERANALYTIC GENERALIZED FUNCTIONS 74 4. SUPERANALOG OF THE THEORY OF SCHWARTZ DISTRIBUTIONS 92 5. THEOREM OF EXISTENCE OF A FUNDAMENTAL SOLUTION . . 100 6. UNSOLVED PROBLEMS AND POSSIBLE GENERALIZATIONS . . . 106 VLLL TABLE OF CONTENTS III DISTRIBUTION THEORY ON AN INFINITE-DIMENSIONAL SU- PERSPACE 109 1. POLYLINEAR ALGEBRA OVER COMMUTATIVE SUPERMODULES 110 2. BANACH SUPERMODULES 116 3. HUBERT SUPERMODULES 130 4. DUALITY OF TOPOLOGICAL SUPERMODULES 141 5. DIFFERENTIAL CALCULUS ON A SUPERSPACE OVER TOPOLOGICAL SUPERMODULES 144 6. ANALYTIC DISTRIBUTIONS ON A SUPERSPACE OVER TOPOLOGI- CAL SUPERMODULES 158 7. GAUSSIAN AND FEYNMAN DISTRIBUTIONS 166 8. UNSOLVED PROBLEMS AND POSSIBLE GENERALIZATIONS ... 180 IV PSEUDODIFFERENTIAL OPERATORS IN SUPERANALYSIS 183 1. PSEUDODIFFERENTIAL OPERATORS CALCULUS 183 2. THE CORRESPONDENCE PRINCIPLE 197 3. THE FEYNMAN-KAC FORMULA FOR THE SYMBOL OF THE EVO- LUTION OPERATOR 205 4. UNSOLVED PROBLEMS AND POSSIBLE GENERALIZATIONS . . . 221 V FUNDAMENTALS OF THE PROBABILITY THEORY ON A SU- PERSPACE 227 1. LIMIT THEOREMS ON A SUPERSPACE 227 2. RANDOM PROCESSES ON A SUPERSPACE 240 3. AXIOMATICS OF THE PROBABILITY THEORY OVER SUPERALGE- BRAS 244 4. UNSOLVED PROBLEMS AND POSSIBLE GENERALIZATIONS . . . 254 VI NON-ARCHIMEDEAN SUPERANALYSIS 257 1. DIFFERENTIABLE AND ANALYTIC FUNCTIONS 258 2. GENERALIZED FUNCTIONS 264 3. LAPLACE TRANSFORMATION 267 4. GAUSSIAN DISTRIBUTIONS 269 5. DUHAMEL NON-ARCHIMEDEAN INTEGRAL. CHRONOLOGICAL EX- PONENT 270 TABLE OF CONTENTS IX 6. CAUCHY PROBLEM FOR PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS 273 7. NON-ARCHIMEDEAN SUPERSYMMETRICAL QUANTUM MECHAN- ICS 276 8. TROTTER FORMULA FOR NON-ARCHIMEDEAN BANACH ALGE- BRAS 278 9. VOLKENBORN DISTRIBUTION ON A NON-ARCHIMEDEAN SUPER- SPACE 279 10. INFINITE-DIMENSIONAL NON-ARCHIMEDEAN SUPERANALYSIS 283 11. UNSOLVED PROBLEMS AND POSSIBLE GENERALIZATIONS . . . 289 VII NONCOMMUTATIVE ANALYSIS 293 1. DIFFERENTIAL CALCULUS ON A SUPERSPACE OVER A NONCOM- MUTATIVE BANACH ALGEBRA 294 2. DIFFERENTIAL CALCULUS ON NONCOMMUTATIVE BANACH AL- GEBRAS AND MODULES 298 3. GENERALIZED FUNCTIONS OF NONCOMMUTING VARIABLES . 309 VIII APPLICATIONS IN PHYSICS 313 1. QUANTIZATION IN HILBERT SUPERMODULES 314 2. TRANSITION AMPLITUDES AND DISTRIBUTIONS ON THE SPACE OF SCHWINGER SOURCES 315 REFERENCES 329 INDEX 345
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author	Khrennikov, Andrei 1958-
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id	DE-604.BV013120093
illustrated	Not Illustrated
indexdate	2024-07-09T18:39:24Z
institution	BVB
isbn	0792356071
language	English
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physical	IX, 347 S.
publishDate	1999
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publishDateSort	1999
publisher	Kluwer Acad. Publ.
record_format	marc
series	Mathematics and its applications
series2	Mathematics and its applications
spelling	Khrennikov, Andrei 1958- Verfasser (DE-588)128568410 aut Superanalysis Superanalysis by Andrei Khrennikov Dordrecht [u.a.] Kluwer Acad. Publ. 1999 IX, 347 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 470 Aus dem Russ. übers. Analysis (DE-588)4001865-9 gnd rswk-swf Superraum (DE-588)4519265-0 gnd rswk-swf Analysis (DE-588)4001865-9 s Superraum (DE-588)4519265-0 s DE-604 Mathematics and its applications 470 (DE-604)BV008163334 470 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008938719&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Khrennikov, Andrei 1958- Superanalysis Mathematics and its applications Analysis (DE-588)4001865-9 gnd Superraum (DE-588)4519265-0 gnd
subject_GND	(DE-588)4001865-9 (DE-588)4519265-0
title	Superanalysis
title_alt	Superanalysis
title_auth	Superanalysis
title_exact_search	Superanalysis
title_full	Superanalysis by Andrei Khrennikov
title_fullStr	Superanalysis by Andrei Khrennikov
title_full_unstemmed	Superanalysis by Andrei Khrennikov
title_short	Superanalysis
title_sort	superanalysis
topic	Analysis (DE-588)4001865-9 gnd Superraum (DE-588)4519265-0 gnd
topic_facet	Analysis Superraum
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008938719&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV008163334
work_keys_str_mv	AT khrennikovandrei superanalysis

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