The convolution product and some applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Romanian |
| Veröffentlicht: |
Bucureşti, Romania
Ed. Academiei u.a.
1982
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Mathematics and its applications / East European series
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Rumän. übers. |
| Beschreibung: | XVII, 332 S. |
| ISBN: | 9027714096 |
Internformat
MARC
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| 240 | 1 | 0 | |a Produsul de convoluţie şi aplicaţii |
| 245 | 1 | 0 | |a The convolution product and some applications |c Wilhelm Kecs |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Bucureşti, Romania |b Ed. Academiei u.a. |c 1982 | |
| 300 | |a XVII, 332 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / East European series |v 2 | |
| 500 | |a Aus dem Rumän. übers. | ||
| 650 | 4 | |a Convolution | |
| 650 | 7 | |a Convolutions (Mathématiques) |2 ram | |
| 650 | 4 | |a Distribution périodique | |
| 650 | 7 | |a Distributions, théorie des (Analyse fonctionnelle) |2 ram | |
| 650 | 4 | |a Electricité | |
| 650 | 4 | |a Equation convolution | |
| 650 | 4 | |a Espace vectoriel topologique | |
| 650 | 7 | |a Espaces vectoriels topologiques |2 ram | |
| 650 | 4 | |a Transformation intégrale | |
| 650 | 4 | |a Viscoélasticité | |
| 650 | 4 | |a Convolutions (Mathematics) | |
| 650 | 4 | |a Linear topological spaces | |
| 650 | 4 | |a Theory of distributions (Functional analysis) | |
| 650 | 0 | 7 | |a Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804114655258345472 |
|---|---|
| adam_text | Table of contents
Editor s Preface xi
Preface to the English edition xiii
Preface to the Romanian edition xv
Note to the Reader xvii
CHAPTER 1 / Topological vector spaces
1.1. Remarkable Sets in Vector Spaces 1
1.1.1. Introduction 1
1.1.2. Remarkable Sets in Vector Spaces 1
1.2. Normed Vector Spaces. Metric Spaces 8
1.2.1. Linear Functionals 8
1.2.2. Seminorm Properties 9
1.3. Topological Vector Spaces 17
1.3.1. Elements of General Topology 17
1.3.2. The Topology of Metric Spaces 19
1.3.3. The Axioms of Topological Vector Spaces. Locally Convex
Spaces 21
1.4. Functional Spaces 26
1.4.1. Functional Classes, Generalities and Notations. The Space
L 26
1.4.2. Fundamental Spaces 33
1.5. The Distribution Space 43
CHAPTER 2 / The convolution product
2.1. The Convolution Product for Functions 61
2.1.1. Convolution in the Spaces U. General Properties .... 61
2.1.2. Regularization and Approximation of Functions Using the
Convolution Product 74
vii
viii TABLE OF CONTENTS
2.1.3. The Convolution Algebra C(R+) 84
2.1.4. Mikusinski s Operational Calculus 95
2.2. The Convolution Product of Distributions 107
2.2.1. The Direct Product of Functions and Distributions.
General Properties 107
2.2.2. The Convolution Product of Distributions. Existence
Criteria. General Properties 113
2.2.3. Regularization and Approximation of Distributions . . . 125
2.2.4. The Convolution of Distribution Depending on a Para¬
meter. The Partial Convolution Product 135
2.2.5. Properties of the Partial Convolution Product 148
CHAPTER 3 / Integral transforms and periodic distributions
3.1. The Fourier Transform of Functions 153
3.1.1. The Fourier Transform of Functions. The Fourier Trans¬
form of the Space S 153
3.1.2. The Fourier Transform of Distributions from the Space S 165
3.2. The Laplace Transform 172
3.2.1. The Laplace Transform of Functions and Distributions . 172
3.3. Periodic Distributions 179
3.3.1. Introduction 179
3.3.2. Periodic Functions, Periodic Transform and Periodic
Partition of Unity 180
3.3.3. Trigonometric Series and Periodic Distribution. The Periodic
Transform of Distributions 186
3.3.4. Fourier Series of Distributions 194
CHAPTER 4 / Convolution Equations
4.1. Convolution Algebras and Equations. General Properties 203
4.2. Convolution Equations in K + 211
4.2.1. The Convolution Algebra in K + 211
4.2.2. The Use of Convolution Algebra K + for Solving Ordinary
Differential Equations 214
4.2.3. Integro Differential Equations of Convolution Type . . 232
4.3. Partial Differential Equations. Fundamental Solutions and
Solution of the Cauchy Initial Value Problem 240
4.4. The Fundamental Solution and the Cauchy Initial Value
Problem for the Wave Equation, Non Distortional Net¬
work Equation and Heat Equation 251
TABLE OF CONTENTS ix
4.4.1. The Wave Equation 251
4.4.2. The Electric Network Equation for Non Distortional
Power Lines 260
4.4.3. The Heat Transfer Equation 263
CHAPTER 5 / Application of the convolution product
5.1. Applications in Electrical Engineering 267
5.1.1. The Volume and Surface Potential of the Electrostatic
Field 267
5.1.2. Inductively Coupled Electric Circuits 271
5.1.3. Quadruples 281
5.2. Applications in Mechanical Engineering 284
5.2.1. Linear Vibrating Systems 284
5.2.2. The Static Problem for the Elastic Continuum. The Funda¬
mental Solution of the Displacements Method 289
5.3. The Viscoelastic Solid 295
5.3.1. The One dimensional Viscoelastic Solid 295
5.3.2. The General Constitutive Law of One dimensional Linear
Viscoelastic Solids 303
5.3.3. The General Equations of Linear Viscoelastic Solids . . 311
References 323
Index 329
|
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| author | Kecs, Wilhelm |
| author_facet | Kecs, Wilhelm |
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| dewey-full | 515.7/82 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.7/82 |
| dewey-sort | 3515.7 282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV000194345 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:10Z |
| institution | BVB |
| isbn | 9027714096 |
| language | English Romanian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000113470 |
| oclc_num | 8805450 |
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| physical | XVII, 332 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Ed. Academiei u.a. |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Kecs, Wilhelm Verfasser aut Produsul de convoluţie şi aplicaţii The convolution product and some applications Wilhelm Kecs 2. ed. Bucureşti, Romania Ed. Academiei u.a. 1982 XVII, 332 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 2 Aus dem Rumän. übers. Convolution Convolutions (Mathématiques) ram Distribution périodique Distributions, théorie des (Analyse fonctionnelle) ram Electricité Equation convolution Espace vectoriel topologique Espaces vectoriels topologiques ram Transformation intégrale Viscoélasticité Convolutions (Mathematics) Linear topological spaces Theory of distributions (Functional analysis) Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Faltung Mathematik (DE-588)4141470-6 gnd rswk-swf Faltungsprodukt (DE-588)7514503-0 gnd rswk-swf Faltungsprodukt (DE-588)7514503-0 s DE-604 Distribution Funktionalanalysis (DE-588)4070505-5 s Faltung Mathematik (DE-588)4141470-6 s 1\p DE-604 East European series Mathematics and its applications 2 (DE-604)BV000006709 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113470&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kecs, Wilhelm The convolution product and some applications Convolution Convolutions (Mathématiques) ram Distribution périodique Distributions, théorie des (Analyse fonctionnelle) ram Electricité Equation convolution Espace vectoriel topologique Espaces vectoriels topologiques ram Transformation intégrale Viscoélasticité Convolutions (Mathematics) Linear topological spaces Theory of distributions (Functional analysis) Distribution Funktionalanalysis (DE-588)4070505-5 gnd Faltung Mathematik (DE-588)4141470-6 gnd Faltungsprodukt (DE-588)7514503-0 gnd |
| subject_GND | (DE-588)4070505-5 (DE-588)4141470-6 (DE-588)7514503-0 |
| title | The convolution product and some applications |
| title_alt | Produsul de convoluţie şi aplicaţii |
| title_auth | The convolution product and some applications |
| title_exact_search | The convolution product and some applications |
| title_full | The convolution product and some applications Wilhelm Kecs |
| title_fullStr | The convolution product and some applications Wilhelm Kecs |
| title_full_unstemmed | The convolution product and some applications Wilhelm Kecs |
| title_short | The convolution product and some applications |
| title_sort | the convolution product and some applications |
| topic | Convolution Convolutions (Mathématiques) ram Distribution périodique Distributions, théorie des (Analyse fonctionnelle) ram Electricité Equation convolution Espace vectoriel topologique Espaces vectoriels topologiques ram Transformation intégrale Viscoélasticité Convolutions (Mathematics) Linear topological spaces Theory of distributions (Functional analysis) Distribution Funktionalanalysis (DE-588)4070505-5 gnd Faltung Mathematik (DE-588)4141470-6 gnd Faltungsprodukt (DE-588)7514503-0 gnd |
| topic_facet | Convolution Convolutions (Mathématiques) Distribution périodique Distributions, théorie des (Analyse fonctionnelle) Electricité Equation convolution Espace vectoriel topologique Espaces vectoriels topologiques Transformation intégrale Viscoélasticité Convolutions (Mathematics) Linear topological spaces Theory of distributions (Functional analysis) Distribution Funktionalanalysis Faltung Mathematik Faltungsprodukt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113470&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
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