Tables of Fourier Transforms and Fourier Transforms of Distributions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These tables represent a new, revised and enlarged version of the previously published book by this author, entitled "Tabellen zur Fourier Transformation" (Springer Verlag 1957). Known errors have been corrected, apart from the addition of a considerable number of new results, which involve almost exclusively higher functions. Again, the following tables contain a collection of integrals of the form J f(x)cos(xy)dx Fourier Cosine Transform (Al o (B) J f(x)sin(xy)dx Fourier Sine Transform o (C) ge(y) = J f(x)eixYdx Exponential Fourier Transform -00 Clearly, (A) and (B) are special cases of (C) if f(x) is respectively an even or an odd function. The transform parameter y in (A) and (B) is assumed to be positive, while in (C) negative values are also included. A possible analytic continuation to complex parameters y* should present no difficulties. In some cases the result function g(y) is given over a partial range of y only. This means that g(y) for the remaining part of y cannot be given in a reasonably simple form. Under certain conditions the following inversion formulas for (A), (B), (C) hold: (A' ) f(x) = 2 J g (y)cos(xy)dy 11 0 c 2 J (B') f (x) gs(y)sin(xy)dy 11 0 -1 00 -ix (C' ) f(x) = (211) J ge(y)e Ydy In the following parts I, II, III tables for the transforms (A), (B) and (C) are given |
| Beschreibung: | 1 Online-Ressource (VIII, 259p) |
| ISBN: | 9783642743498 9783540506300 |
| DOI: | 10.1007/978-3-642-74349-8 |
Internformat
MARC
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| 500 | |a These tables represent a new, revised and enlarged version of the previously published book by this author, entitled "Tabellen zur Fourier Transformation" (Springer Verlag 1957). Known errors have been corrected, apart from the addition of a considerable number of new results, which involve almost exclusively higher functions. Again, the following tables contain a collection of integrals of the form J f(x)cos(xy)dx Fourier Cosine Transform (Al o (B) J f(x)sin(xy)dx Fourier Sine Transform o (C) ge(y) = J f(x)eixYdx Exponential Fourier Transform -00 Clearly, (A) and (B) are special cases of (C) if f(x) is respectively an even or an odd function. The transform parameter y in (A) and (B) is assumed to be positive, while in (C) negative values are also included. A possible analytic continuation to complex parameters y* should present no difficulties. In some cases the result function g(y) is given over a partial range of y only. This means that g(y) for the remaining part of y cannot be given in a reasonably simple form. Under certain conditions the following inversion formulas for (A), (B), (C) hold: (A' ) f(x) = 2 J g (y)cos(xy)dy 11 0 c 2 J (B') f (x) gs(y)sin(xy)dy 11 0 -1 00 -ix (C' ) f(x) = (211) J ge(y)e Ydy In the following parts I, II, III tables for the transforms (A), (B) and (C) are given | ||
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| 650 | 4 | |a Topological Groups | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Oberhettinger, Fritz |
| author_facet | Oberhettinger, Fritz |
| author_role | aut |
| author_sort | Oberhettinger, Fritz |
| author_variant | f o fo |
| building | Verbundindex |
| bvnumber | BV042422973 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-74349-8 |
| format | Electronic eBook |
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| isbn | 9783642743498 9783540506300 |
| language | English |
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| spelling | Oberhettinger, Fritz Verfasser aut Tables of Fourier Transforms and Fourier Transforms of Distributions by Fritz Oberhettinger Berlin, Heidelberg Springer Berlin Heidelberg 1990 1 Online-Ressource (VIII, 259p) txt rdacontent c rdamedia cr rdacarrier These tables represent a new, revised and enlarged version of the previously published book by this author, entitled "Tabellen zur Fourier Transformation" (Springer Verlag 1957). Known errors have been corrected, apart from the addition of a considerable number of new results, which involve almost exclusively higher functions. Again, the following tables contain a collection of integrals of the form J f(x)cos(xy)dx Fourier Cosine Transform (Al o (B) J f(x)sin(xy)dx Fourier Sine Transform o (C) ge(y) = J f(x)eixYdx Exponential Fourier Transform -00 Clearly, (A) and (B) are special cases of (C) if f(x) is respectively an even or an odd function. The transform parameter y in (A) and (B) is assumed to be positive, while in (C) negative values are also included. A possible analytic continuation to complex parameters y* should present no difficulties. In some cases the result function g(y) is given over a partial range of y only. This means that g(y) for the remaining part of y cannot be given in a reasonably simple form. Under certain conditions the following inversion formulas for (A), (B), (C) hold: (A' ) f(x) = 2 J g (y)cos(xy)dy 11 0 c 2 J (B') f (x) gs(y)sin(xy)dy 11 0 -1 00 -ix (C' ) f(x) = (211) J ge(y)e Ydy In the following parts I, II, III tables for the transforms (A), (B) and (C) are given Mathematics Topological Groups Distribution (Probability theory) Mathematical physics Engineering mathematics Topological Groups, Lie Groups Real Functions Probability Theory and Stochastic Processes Appl.Mathematics/Computational Methods of Engineering Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf 1\p (DE-588)4184335-6 Tafel gnd-content 2\p (DE-588)4184303-4 Tabelle gnd-content Fourier-Transformation (DE-588)4018014-1 s 3\p DE-604 https://doi.org/10.1007/978-3-642-74349-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Oberhettinger, Fritz Tables of Fourier Transforms and Fourier Transforms of Distributions Mathematics Topological Groups Distribution (Probability theory) Mathematical physics Engineering mathematics Topological Groups, Lie Groups Real Functions Probability Theory and Stochastic Processes Appl.Mathematics/Computational Methods of Engineering Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4018014-1 (DE-588)4184335-6 (DE-588)4184303-4 |
| title | Tables of Fourier Transforms and Fourier Transforms of Distributions |
| title_auth | Tables of Fourier Transforms and Fourier Transforms of Distributions |
| title_exact_search | Tables of Fourier Transforms and Fourier Transforms of Distributions |
| title_full | Tables of Fourier Transforms and Fourier Transforms of Distributions by Fritz Oberhettinger |
| title_fullStr | Tables of Fourier Transforms and Fourier Transforms of Distributions by Fritz Oberhettinger |
| title_full_unstemmed | Tables of Fourier Transforms and Fourier Transforms of Distributions by Fritz Oberhettinger |
| title_short | Tables of Fourier Transforms and Fourier Transforms of Distributions |
| title_sort | tables of fourier transforms and fourier transforms of distributions |
| topic | Mathematics Topological Groups Distribution (Probability theory) Mathematical physics Engineering mathematics Topological Groups, Lie Groups Real Functions Probability Theory and Stochastic Processes Appl.Mathematics/Computational Methods of Engineering Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Mathematics Topological Groups Distribution (Probability theory) Mathematical physics Engineering mathematics Topological Groups, Lie Groups Real Functions Probability Theory and Stochastic Processes Appl.Mathematics/Computational Methods of Engineering Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Fourier-Transformation Tafel Tabelle |
| url | https://doi.org/10.1007/978-3-642-74349-8 |
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