Integral Transformations, Operational Calculus, and Generalized Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1996
|
| Schriftenreihe: | Mathematics and Its Applications
377 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | It is not the object of the author to present comprehensive coverage of any particular integral transformation or of any particular development of generalized functions, for there are books available in which this is done. Rather, this consists more of an introductory survey in which various ideas are explored. The Laplace transformation is taken as the model type of an integral transformation and a number of its properties are developed; later, the Fourier transformation is introduced. The operational calculus of Mikusinski is presented as a method of introducing generalized functions associated with the Laplace transformation. The construction is analogous to the construction of the rational numbers from the integers. Further on, generalized functions associated with the problem of extension of the Fourier transformation are introduced. This construction is analogous to the construction of the reals from the rationals by means of Cauchy sequences. A chapter with sections on a variety of transformations is adjoined. Necessary levels of sophistication start low in the first chapter, but they grow considerably in some sections of later chapters. Background needs are stated at the beginnings of each chapter. Many theorems are given without proofs, which seems appropriate for the goals in mind. A selection of references is included. Without showing many of the details of rigor it is hoped that a strong indication is given that a firm mathematical foundation does actually exist for such entities as the "Dirac delta-function" |
| Beschreibung: | 1 Online-Ressource (XIV, 240 p) |
| ISBN: | 9781461312833 9781461285489 |
| DOI: | 10.1007/978-1-4613-1283-3 |
Internformat
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| 490 | 1 | |a Mathematics and Its Applications |v 377 | |
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Datensatz im Suchindex
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| dewey-full | 515.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.72 |
| dewey-search | 515.72 |
| dewey-sort | 3515.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-1283-3 |
| format | Electronic eBook |
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| id | DE-604.BV042420610 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461312833 9781461285489 |
| language | English |
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| physical | 1 Online-Ressource (XIV, 240 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Springer US |
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| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Buschman, R. G. Verfasser aut Integral Transformations, Operational Calculus, and Generalized Functions by R. G. Buschman Boston, MA Springer US 1996 1 Online-Ressource (XIV, 240 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 377 It is not the object of the author to present comprehensive coverage of any particular integral transformation or of any particular development of generalized functions, for there are books available in which this is done. Rather, this consists more of an introductory survey in which various ideas are explored. The Laplace transformation is taken as the model type of an integral transformation and a number of its properties are developed; later, the Fourier transformation is introduced. The operational calculus of Mikusinski is presented as a method of introducing generalized functions associated with the Laplace transformation. The construction is analogous to the construction of the rational numbers from the integers. Further on, generalized functions associated with the problem of extension of the Fourier transformation are introduced. This construction is analogous to the construction of the reals from the rationals by means of Cauchy sequences. A chapter with sections on a variety of transformations is adjoined. Necessary levels of sophistication start low in the first chapter, but they grow considerably in some sections of later chapters. Background needs are stated at the beginnings of each chapter. Many theorems are given without proofs, which seems appropriate for the goals in mind. A selection of references is included. Without showing many of the details of rigor it is hoped that a strong indication is given that a firm mathematical foundation does actually exist for such entities as the "Dirac delta-function" Mathematics Integral Transforms Integral Transforms, Operational Calculus Mathematik Integraltransformation (DE-588)4027235-7 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s 1\p DE-604 Mathematics and Its Applications 377 (DE-604)BV008163334 377 https://doi.org/10.1007/978-1-4613-1283-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Buschman, R. G. Integral Transformations, Operational Calculus, and Generalized Functions Mathematics and Its Applications Mathematics Integral Transforms Integral Transforms, Operational Calculus Mathematik Integraltransformation (DE-588)4027235-7 gnd |
| subject_GND | (DE-588)4027235-7 |
| title | Integral Transformations, Operational Calculus, and Generalized Functions |
| title_auth | Integral Transformations, Operational Calculus, and Generalized Functions |
| title_exact_search | Integral Transformations, Operational Calculus, and Generalized Functions |
| title_full | Integral Transformations, Operational Calculus, and Generalized Functions by R. G. Buschman |
| title_fullStr | Integral Transformations, Operational Calculus, and Generalized Functions by R. G. Buschman |
| title_full_unstemmed | Integral Transformations, Operational Calculus, and Generalized Functions by R. G. Buschman |
| title_short | Integral Transformations, Operational Calculus, and Generalized Functions |
| title_sort | integral transformations operational calculus and generalized functions |
| topic | Mathematics Integral Transforms Integral Transforms, Operational Calculus Mathematik Integraltransformation (DE-588)4027235-7 gnd |
| topic_facet | Mathematics Integral Transforms Integral Transforms, Operational Calculus Mathematik Integraltransformation |
| url | https://doi.org/10.1007/978-1-4613-1283-3 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT buschmanrg integraltransformationsoperationalcalculusandgeneralizedfunctions |