Fourier and Wavelet Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2000
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | globalized Fejer's theorem; he showed that the Fourier series for any f E Ld-7I", 7I"] converges (C, 1) to f (t) a.e. The desire to do this was part of the reason that Lebesgue invented his integral; the theorem mentioned above was one of the first uses he made of it (Sec. 4.18). Denjoy, with the same motivation, extended the integral even further. Concurrently, the emerging point of view that things could be decom posed into waves and then reconstituted infused not just mathematics but all of science. It is impossible to quantify the role that this perspective played in the development of the physics of the nineteenth and twentieth centuries, but it was certainly great. Imagine physics without it. We develop the standard features of Fourier analysis-Fourier series, Fourier transform, Fourier sine and cosine transforms. We do NOT do it in the most elegant way. Instead, we develop it for the reader who has never seen them before. We cover more recent developments such as the discrete and fast Fourier transforms and wavelets in Chapters 6 and 7. Our treatment of these topics is strictly introductory, for the novice. (Wavelets for idiots?) To do them properly, especially the applications, would take at least a whole book |
| Beschreibung: | 1 Online-Ressource (IX, 507 p) |
| ISBN: | 9781461205050 9781461267935 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4612-0505-0 |
Internformat
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| 500 | |a globalized Fejer's theorem; he showed that the Fourier series for any f E Ld-7I", 7I"] converges (C, 1) to f (t) a.e. The desire to do this was part of the reason that Lebesgue invented his integral; the theorem mentioned above was one of the first uses he made of it (Sec. 4.18). Denjoy, with the same motivation, extended the integral even further. Concurrently, the emerging point of view that things could be decom posed into waves and then reconstituted infused not just mathematics but all of science. It is impossible to quantify the role that this perspective played in the development of the physics of the nineteenth and twentieth centuries, but it was certainly great. Imagine physics without it. We develop the standard features of Fourier analysis-Fourier series, Fourier transform, Fourier sine and cosine transforms. We do NOT do it in the most elegant way. Instead, we develop it for the reader who has never seen them before. We cover more recent developments such as the discrete and fast Fourier transforms and wavelets in Chapters 6 and 7. Our treatment of these topics is strictly introductory, for the novice. (Wavelets for idiots?) To do them properly, especially the applications, would take at least a whole book | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Bachman, George |
| author_facet | Bachman, George |
| author_role | aut |
| author_sort | Bachman, George |
| author_variant | g b gb |
| building | Verbundindex |
| bvnumber | BV042419542 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0505-0 |
| format | Electronic eBook |
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| id | DE-604.BV042419542 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461205050 9781461267935 |
| issn | 0172-5939 |
| language | English |
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| publishDate | 2000 |
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| spelling | Bachman, George Verfasser aut Fourier and Wavelet Analysis by George Bachman, Lawrence Narici, Edward Beckenstein New York, NY Springer New York 2000 1 Online-Ressource (IX, 507 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 globalized Fejer's theorem; he showed that the Fourier series for any f E Ld-7I", 7I"] converges (C, 1) to f (t) a.e. The desire to do this was part of the reason that Lebesgue invented his integral; the theorem mentioned above was one of the first uses he made of it (Sec. 4.18). Denjoy, with the same motivation, extended the integral even further. Concurrently, the emerging point of view that things could be decom posed into waves and then reconstituted infused not just mathematics but all of science. It is impossible to quantify the role that this perspective played in the development of the physics of the nineteenth and twentieth centuries, but it was certainly great. Imagine physics without it. We develop the standard features of Fourier analysis-Fourier series, Fourier transform, Fourier sine and cosine transforms. We do NOT do it in the most elegant way. Instead, we develop it for the reader who has never seen them before. We cover more recent developments such as the discrete and fast Fourier transforms and wavelets in Chapters 6 and 7. Our treatment of these topics is strictly introductory, for the novice. (Wavelets for idiots?) To do them properly, especially the applications, would take at least a whole book Mathematics Topological Groups Global analysis (Mathematics) Analysis Topological Groups, Lie Groups Mathematik Wavelet (DE-588)4215427-3 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Wavelet (DE-588)4215427-3 s Fourier-Reihe (DE-588)4155109-6 s 1\p DE-604 Fourier-Transformation (DE-588)4018014-1 s 2\p DE-604 Harmonische Analyse (DE-588)4023453-8 s 3\p DE-604 Narici, Lawrence Sonstige oth Beckenstein, Edward Sonstige oth https://doi.org/10.1007/978-1-4612-0505-0 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 | Bachman, George Fourier and Wavelet Analysis Mathematics Topological Groups Global analysis (Mathematics) Analysis Topological Groups, Lie Groups Mathematik Wavelet (DE-588)4215427-3 gnd Fourier-Reihe (DE-588)4155109-6 gnd Fourier-Transformation (DE-588)4018014-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4215427-3 (DE-588)4155109-6 (DE-588)4018014-1 (DE-588)4023453-8 |
| title | Fourier and Wavelet Analysis |
| title_auth | Fourier and Wavelet Analysis |
| title_exact_search | Fourier and Wavelet Analysis |
| title_full | Fourier and Wavelet Analysis by George Bachman, Lawrence Narici, Edward Beckenstein |
| title_fullStr | Fourier and Wavelet Analysis by George Bachman, Lawrence Narici, Edward Beckenstein |
| title_full_unstemmed | Fourier and Wavelet Analysis by George Bachman, Lawrence Narici, Edward Beckenstein |
| title_short | Fourier and Wavelet Analysis |
| title_sort | fourier and wavelet analysis |
| topic | Mathematics Topological Groups Global analysis (Mathematics) Analysis Topological Groups, Lie Groups Mathematik Wavelet (DE-588)4215427-3 gnd Fourier-Reihe (DE-588)4155109-6 gnd Fourier-Transformation (DE-588)4018014-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Mathematics Topological Groups Global analysis (Mathematics) Analysis Topological Groups, Lie Groups Mathematik Wavelet Fourier-Reihe Fourier-Transformation Harmonische Analyse |
| url | https://doi.org/10.1007/978-1-4612-0505-0 |
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