Operational calculus and related topics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2006
|
| Schriftenreihe: | Analytical methods and special functions
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 403 S. graph. Darst. |
| ISBN: | 1584886498 9781584886495 |
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| adam_text | OPERATIONAL CAICULUS AND RELATED TOPICS H.-J. GLAESKE FRIEDRICH-SCHILLER
UNIVERSITY JENA, GERMANY A.R PRUDNIKOV (DECEASED) K.A. SKOERNIK INSTITUTE
OF MATHEMATICS POLISH ACADEMY OF SCIENCES KATOWICE, POLAND CHAPMAN &.
HALL/CRC TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CHAPMAN &
HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA
BUSINESS CONTENTS PREFACE XI LIST OF SYMBOLS XV 1 INTEGRAL TRANSFORMS 1
1.1 INTRODUCTION TO OPERATIONAL CALCULUS 1 1.2 INTEGRAL TRANSFORMS -
INTRODUCTORY REMARKS 5 1.3 THE FOURIER TRANSFORM 8 1.3.1 DEFINITION AND
BASIC PROPERTIES 8 1.3.2 EXAMPLES 11 1.3.3 OPERATIONAL PROPERTIES 13
1.3.4 THE INVERSION FORMULA 17 1.3.5 APPLICATIONS 21 1.4 THE LAPLACE
TRANSFORM 27 1.4.1 DEFINITION AND BASIC PROPERTIES 27 1.4.2 EXAMPLES 31
1.4.3 OPERATIONAL PROPERTIES 33 1.4.4 THE COMPLEX INVERSION FORMULA 37
1.4.5 INVERSION METHODS 40 1.4.6 ASYMPTOTIC BEHAVIOR 44 1.4.7 REMARKS ON
THE BILATERAL LAPLACE TRANSFORM 47 1.4.8 APPLICATIONS 49 1.5 THE MELLIN
TRANSFORM 55 1.5.1 DEFINITION AND BASIC PROPERTIES 55 1.5.2 OPERATIONAL
PROPERTIES 58 1.5.3 THE COMPLEX INVERSION FORMULA 62 1.5.4 APPLICATIONS
63 1.6 THE STIELTJES TRANSFORM 67 1.6.1 DEFINITION AND BASIC PROPERTIES
67 1.6.2 OPERATIONAL PROPERTIES 70 1.6.3 ASYMPTOTICS 73 1.6.4 INVERSION
AND APPLICATION 75 VLLL 1.7 THE HUBERT TRANSFORM 78 1.7.1 DEFINITION AND
BASIC PROPERTIES 78 1.7.2 OPERATIONAL PROPERTIES 81 1.7.3 APPLICATIONS
83 1.8 BESSEL TRANSFORMS 84 1.8.1 THE HANKEL TRANSFORM 85 1.8.2 THE
MEIJER (K-) TRANSFORM 93 1.8.3 THE KONTOROVICH-LEBEDEV TRANSFORM 100
1.8.4 APPLICATION 106 1.9 THE MEHLER-FOCK TRANSFORM 107 1.10 FINITE
INTEGRAL TRANSFORMS 115 1.10.1 INTRODUCTION 115 1.10.2 THE CHEBYSHEV
TRANSFORM 116 1.10.3 THE LEGENDRE TRANSFORM 122 1.10.4 THE GEGENBAUER
TRANSFORM 131 1.10.5 THE JACOBI TRANSFORM 137 1.10.6 THE LAGUERRE
TRANSFORM 144 1.10.7 THE HERMITE TRANSFORM 153 2 OPERATIONAL CALCULUS
163 2.1 INTRODUCTION 163 2.2 TITCHMARSH S THEOREM 167 2.3 OPERATORS 180
2.3.1 RING OF FUNCTIONS 180 2.3.2 THE FIELD OF OPERATORS 185 2.3.3
FINITE PARTS OF DIVERGENT INTEGRALS 190 2.3.4 RATIONAL OPERATORS 201
2.3.5 LAPLACE TRANSFORMABLE OPERATORS 205 2.3.6 EXAMPLES 213 2.3.7
PERIODIC FUNCTIONS 217 2.4 BASES OF THE OPERATOR ANALYSIS 219 2.4.1
SEQUENCES AND SERIES OF OPERATORS 219 2.4.2 OPERATOR FUNCTIONS 226 2.4.3
THE DERIVATIVE OF AN OPERATOR FUNCTION 229 2.4.4 PROPERTIES OF THE
CONTINUOUS DERIVATIVE OF AN OPERATOR FUNCTION . . 229 2.4.5 THE INTEGRAL
OF AN OPERATOR FUNCTION 232 2.5 OPERATORS REDUCIBLE TO FUNCTIONS 236
2.5.1 REGULAER OPERATORS 236 IX 2.5.2 THE REALIZATION OF SOME OPERATORS
239 2.5.3 EFROS TRANSFORMS 242 2.6 APPLICATION OF OPERATIONAL CALCULUS
247 2.6.1 ORDINARY DIFFERENTIAL EQUATIONS 247 2.6.2 PARTIAL DIFFERENTIAL
EQUATIONS 258 3 GENERALIZED FUNCTIONS 271 3.1 INTRODUCTION 271 3.2
GENERALIZED FUNCTIONS * FUNCTIONAL APPROACH 272 3.2.1 INTRODUCTION 272
3.2.2 DISTRIBUTIONS OF ONE VARIABLE 274 3.2.3 DISTRIBUTIONAL CONVERGENCE
279 3.2.4 ALGEBRAIC OPERATIONS ON DISTRIBUTIONS 280 3.3 GENERALIZED
FUNCTIONS * SEQUENTIAL APPROACH 287 3.3.1 THE IDENTIFICATION PRINCIPLE
287 3.3.2 FUNDAMENTAL SEQUENCES 289 3.3.3 DEFINITION OF DISTRIBUTIONS
297 3.3.4 OPERATIONS WITH DISTRIBUTIONS 300 3.3.5 REGULAER OPERATIONS 303
3.4 DELTA SEQUENCES . 311 3.4.1 DEFINITION AND PROPERTIES 311 3.4.2
DISTRIBUTIONS AS A GENERALIZATION OF CONTINUOUS FUNCTIONS . 317 3.4.3
DISTRIBUTIONS AS A GENERALIZATION OF LOCALLY INTEGRABLE FUNCTIONS . .
320 3.4.4 REMARKS ABOUT DISTRIBUTIONAL DERIVATIVES 322 3.4.5 FUNCTIONS
WITH POLES 325 3.4.6 APPLICATIONS 326 3.5 CONVERGENT SEQUENCES 332 3.5.1
SEQUENCES OF DISTRIBUTIONS 332 3.5.2 CONVERGENCE AND REGULAER OPERATIONS
339 3.5.3 DISTRIBUTIONALLY CONVERGENT SEQUENCES OF SMOOTH FUNCTIONS 341
3.5.4 CONVOLUTION OF DISTRIBUTION WITH A SMOOTH FUNCTION OF BOUNDED SUP-
PORT 344 3.5.5 APPLICATIONS 346 3.6 LOCAL PROPERTIES 347 3.6.1 INNER
PRODUCT OF TWO FUNCTIONS 347 3.6.2 DISTRIBUTIONS OF FINITE ORDER 350
3.6.3 THE VALUE OF A DISTRIBUTION AT A POINT 352 3.6.4 THE VALUE OF A
DISTRIBUTION AT INFINITY 355 X 3.6.5 SUPPORT OF A DISTRIBUTION 355 3.7
IRREGULAER OPERATIONS 355 3.7.1 DEFINITION 355 3.7.2 THE INTEGRAL OF
DISTRIBUTIONS 357 3.7.3 CONVOLUTION OF DISTRIBUTIONS 369 3.7.4
MULTIPLICATION OF DISTRIBUTIONS 375 3.7.5 APPLICATIONS 379 3.8 HILBERT
TRANSFORM AND MULTIPLICATION FORMS 381 3.8.1 DEFINITION OF THE HILBERT
TRANSFORM 381 3.8.2 APPLICATIONS AND EXAMPLES 383 REFERENCES 389 INDEX
401
|
| adam_txt |
OPERATIONAL CAICULUS AND RELATED TOPICS H.-J. GLAESKE FRIEDRICH-SCHILLER
UNIVERSITY JENA, GERMANY A.R PRUDNIKOV (DECEASED) K.A. SKOERNIK INSTITUTE
OF MATHEMATICS POLISH ACADEMY OF SCIENCES KATOWICE, POLAND CHAPMAN &.
HALL/CRC TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CHAPMAN &
HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA
BUSINESS CONTENTS PREFACE XI LIST OF SYMBOLS XV 1 INTEGRAL TRANSFORMS 1
1.1 INTRODUCTION TO OPERATIONAL CALCULUS 1 1.2 INTEGRAL TRANSFORMS -
INTRODUCTORY REMARKS 5 1.3 THE FOURIER TRANSFORM 8 1.3.1 DEFINITION AND
BASIC PROPERTIES 8 1.3.2 EXAMPLES 11 1.3.3 OPERATIONAL PROPERTIES 13
1.3.4 THE INVERSION FORMULA 17 1.3.5 APPLICATIONS 21 1.4 THE LAPLACE
TRANSFORM 27 1.4.1 DEFINITION AND BASIC PROPERTIES 27 1.4.2 EXAMPLES 31
1.4.3 OPERATIONAL PROPERTIES 33 1.4.4 THE COMPLEX INVERSION FORMULA 37
1.4.5 INVERSION METHODS 40 1.4.6 ASYMPTOTIC BEHAVIOR 44 1.4.7 REMARKS ON
THE BILATERAL LAPLACE TRANSFORM 47 1.4.8 APPLICATIONS 49 1.5 THE MELLIN
TRANSFORM 55 1.5.1 DEFINITION AND BASIC PROPERTIES 55 1.5.2 OPERATIONAL
PROPERTIES 58 1.5.3 THE COMPLEX INVERSION FORMULA 62 1.5.4 APPLICATIONS
63 1.6 THE STIELTJES TRANSFORM 67 1.6.1 DEFINITION AND BASIC PROPERTIES
67 1.6.2 OPERATIONAL PROPERTIES 70 1.6.3 ASYMPTOTICS 73 1.6.4 INVERSION
AND APPLICATION 75 VLLL 1.7 THE HUBERT TRANSFORM 78 1.7.1 DEFINITION AND
BASIC PROPERTIES 78 1.7.2 OPERATIONAL PROPERTIES 81 1.7.3 APPLICATIONS
83 1.8 BESSEL TRANSFORMS 84 1.8.1 THE HANKEL TRANSFORM 85 1.8.2 THE
MEIJER (K-) TRANSFORM 93 1.8.3 THE KONTOROVICH-LEBEDEV TRANSFORM 100
1.8.4 APPLICATION 106 1.9 THE MEHLER-FOCK TRANSFORM 107 1.10 FINITE
INTEGRAL TRANSFORMS 115 1.10.1 INTRODUCTION 115 1.10.2 THE CHEBYSHEV
TRANSFORM 116 1.10.3 THE LEGENDRE TRANSFORM 122 1.10.4 THE GEGENBAUER
TRANSFORM 131 1.10.5 THE JACOBI TRANSFORM 137 1.10.6 THE LAGUERRE
TRANSFORM 144 1.10.7 THE HERMITE TRANSFORM 153 2 OPERATIONAL CALCULUS
163 2.1 INTRODUCTION 163 2.2 TITCHMARSH'S THEOREM 167 2.3 OPERATORS 180
2.3.1 RING OF FUNCTIONS 180 2.3.2 THE FIELD OF OPERATORS 185 2.3.3
FINITE PARTS OF DIVERGENT INTEGRALS 190 2.3.4 RATIONAL OPERATORS 201
2.3.5 LAPLACE TRANSFORMABLE OPERATORS 205 2.3.6 EXAMPLES 213 2.3.7
PERIODIC FUNCTIONS 217 2.4 BASES OF THE OPERATOR ANALYSIS 219 2.4.1
SEQUENCES AND SERIES OF OPERATORS 219 2.4.2 OPERATOR FUNCTIONS 226 2.4.3
THE DERIVATIVE OF AN OPERATOR FUNCTION 229 2.4.4 PROPERTIES OF THE
CONTINUOUS DERIVATIVE OF AN OPERATOR FUNCTION . . 229 2.4.5 THE INTEGRAL
OF AN OPERATOR FUNCTION 232 2.5 OPERATORS REDUCIBLE TO FUNCTIONS 236
2.5.1 REGULAER OPERATORS 236 IX 2.5.2 THE REALIZATION OF SOME OPERATORS
239 2.5.3 EFROS TRANSFORMS 242 2.6 APPLICATION OF OPERATIONAL CALCULUS
247 2.6.1 ORDINARY DIFFERENTIAL EQUATIONS 247 2.6.2 PARTIAL DIFFERENTIAL
EQUATIONS 258 3 GENERALIZED FUNCTIONS 271 3.1 INTRODUCTION 271 3.2
GENERALIZED FUNCTIONS * FUNCTIONAL APPROACH 272 3.2.1 INTRODUCTION 272
3.2.2 DISTRIBUTIONS OF ONE VARIABLE 274 3.2.3 DISTRIBUTIONAL CONVERGENCE
279 3.2.4 ALGEBRAIC OPERATIONS ON DISTRIBUTIONS 280 3.3 GENERALIZED
FUNCTIONS * SEQUENTIAL APPROACH 287 3.3.1 THE IDENTIFICATION PRINCIPLE
287 3.3.2 FUNDAMENTAL SEQUENCES 289 3.3.3 DEFINITION OF DISTRIBUTIONS
297 3.3.4 OPERATIONS WITH DISTRIBUTIONS 300 3.3.5 REGULAER OPERATIONS 303
3.4 DELTA SEQUENCES .' 311 3.4.1 DEFINITION AND PROPERTIES 311 3.4.2
DISTRIBUTIONS AS A GENERALIZATION OF CONTINUOUS FUNCTIONS '. 317 3.4.3
DISTRIBUTIONS AS A GENERALIZATION OF LOCALLY INTEGRABLE FUNCTIONS . .
320 3.4.4 REMARKS ABOUT DISTRIBUTIONAL DERIVATIVES 322 3.4.5 FUNCTIONS
WITH POLES 325 3.4.6 APPLICATIONS 326 3.5 CONVERGENT SEQUENCES 332 3.5.1
SEQUENCES OF DISTRIBUTIONS 332 3.5.2 CONVERGENCE AND REGULAER OPERATIONS
339 3.5.3 DISTRIBUTIONALLY CONVERGENT SEQUENCES OF SMOOTH FUNCTIONS 341
3.5.4 CONVOLUTION OF DISTRIBUTION WITH A SMOOTH FUNCTION OF BOUNDED SUP-
PORT 344 3.5.5 APPLICATIONS 346 3.6 LOCAL PROPERTIES 347 3.6.1 INNER
PRODUCT OF TWO FUNCTIONS 347 3.6.2 DISTRIBUTIONS OF FINITE ORDER 350
3.6.3 THE VALUE OF A DISTRIBUTION AT A POINT 352 3.6.4 THE VALUE OF A
DISTRIBUTION AT INFINITY 355 X 3.6.5 SUPPORT OF A DISTRIBUTION 355 3.7
IRREGULAER OPERATIONS 355 3.7.1 DEFINITION 355 3.7.2 THE INTEGRAL OF
DISTRIBUTIONS 357 3.7.3 CONVOLUTION OF DISTRIBUTIONS 369 3.7.4
MULTIPLICATION OF DISTRIBUTIONS 375 3.7.5 APPLICATIONS 379 3.8 HILBERT
TRANSFORM AND MULTIPLICATION FORMS 381 3.8.1 DEFINITION OF THE HILBERT
TRANSFORM 381 3.8.2 APPLICATIONS AND EXAMPLES 383 REFERENCES 389 INDEX
401 |
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| index_date | 2024-07-02T14:52:00Z |
| indexdate | 2024-07-09T20:39:57Z |
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| series | Analytical methods and special functions |
| series2 | Analytical methods and special functions |
| spelling | Glaeske, Hans-Jürgen Verfasser aut Operational calculus and related topics H.-J. Glaeske, A.P. Prudnikov, K.A. Skórnik Boca Raton [u.a.] Chapman & Hall/CRC 2006 XVI, 403 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analytical methods and special functions 10 Calculus, Operational Transformations (Mathematics) Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Distributionstheorie (DE-588)4150254-1 s Transformation Mathematik (DE-588)4060637-5 s DE-604 Prudnikov, Anatolij Platonovič Sonstige oth Skórnik, Krystyna Sonstige oth Analytical methods and special functions 10 (DE-604)BV011932737 10 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014830480&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Glaeske, Hans-Jürgen Operational calculus and related topics Analytical methods and special functions Calculus, Operational Transformations (Mathematics) Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd Operatortheorie (DE-588)4075665-8 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| subject_GND | (DE-588)4150254-1 (DE-588)4075665-8 (DE-588)4060637-5 |
| title | Operational calculus and related topics |
| title_auth | Operational calculus and related topics |
| title_exact_search | Operational calculus and related topics |
| title_exact_search_txtP | Operational calculus and related topics |
| title_full | Operational calculus and related topics H.-J. Glaeske, A.P. Prudnikov, K.A. Skórnik |
| title_fullStr | Operational calculus and related topics H.-J. Glaeske, A.P. Prudnikov, K.A. Skórnik |
| title_full_unstemmed | Operational calculus and related topics H.-J. Glaeske, A.P. Prudnikov, K.A. Skórnik |
| title_short | Operational calculus and related topics |
| title_sort | operational calculus and related topics |
| topic | Calculus, Operational Transformations (Mathematics) Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd Operatortheorie (DE-588)4075665-8 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| topic_facet | Calculus, Operational Transformations (Mathematics) Theory of distributions (Functional analysis) Distributionstheorie Operatortheorie Transformation Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014830480&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932737 |
| work_keys_str_mv | AT glaeskehansjurgen operationalcalculusandrelatedtopics AT prudnikovanatolijplatonovic operationalcalculusandrelatedtopics AT skornikkrystyna operationalcalculusandrelatedtopics |