The Uncertainty Principle in Harmonic Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics
28 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose) |
| Beschreibung: | 1 Online-Ressource (XII, 547p) |
| ISBN: | 9783642783777 9783642783791 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-78377-7 |
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Datensatz im Suchindex
| _version_ | 1804153098189406208 |
|---|---|
| any_adam_object | |
| author | Havin, Victor |
| author_facet | Havin, Victor |
| author_role | aut |
| author_sort | Havin, Victor |
| author_variant | v h vh |
| building | Verbundindex |
| bvnumber | BV042423003 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)863857959 (DE-599)BVBBV042423003 |
| dewey-full | 515.785 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.785 |
| dewey-search | 515.785 |
| dewey-sort | 3515.785 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-78377-7 |
| format | Electronic eBook |
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| id | DE-604.BV042423003 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642783777 9783642783791 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858420 |
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| publishDate | 1994 |
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| publishDateSort | 1994 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics |
| spelling | Havin, Victor Verfasser aut The Uncertainty Principle in Harmonic Analysis by Victor Havin, Burglind Jöricke Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (XII, 547p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics 28 0071-1136 The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose) Mathematics Harmonic analysis Fourier analysis Abstract Harmonic Analysis Fourier Analysis Theoretical, Mathematical and Computational Physics Mathematik Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Unsicherheit (DE-588)4186957-6 gnd rswk-swf Unschärfe (DE-588)4273405-8 gnd rswk-swf Unschärferelation (DE-588)4186953-9 gnd rswk-swf Unschärferelation (DE-588)4186953-9 s Harmonische Analyse (DE-588)4023453-8 s 1\p DE-604 Unschärfe (DE-588)4273405-8 s 2\p DE-604 Unsicherheit (DE-588)4186957-6 s 3\p DE-604 Jöricke, Burglind Sonstige oth https://doi.org/10.1007/978-3-642-78377-7 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 | Havin, Victor The Uncertainty Principle in Harmonic Analysis Mathematics Harmonic analysis Fourier analysis Abstract Harmonic Analysis Fourier Analysis Theoretical, Mathematical and Computational Physics Mathematik Harmonische Analyse (DE-588)4023453-8 gnd Unsicherheit (DE-588)4186957-6 gnd Unschärfe (DE-588)4273405-8 gnd Unschärferelation (DE-588)4186953-9 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4186957-6 (DE-588)4273405-8 (DE-588)4186953-9 |
| title | The Uncertainty Principle in Harmonic Analysis |
| title_auth | The Uncertainty Principle in Harmonic Analysis |
| title_exact_search | The Uncertainty Principle in Harmonic Analysis |
| title_full | The Uncertainty Principle in Harmonic Analysis by Victor Havin, Burglind Jöricke |
| title_fullStr | The Uncertainty Principle in Harmonic Analysis by Victor Havin, Burglind Jöricke |
| title_full_unstemmed | The Uncertainty Principle in Harmonic Analysis by Victor Havin, Burglind Jöricke |
| title_short | The Uncertainty Principle in Harmonic Analysis |
| title_sort | the uncertainty principle in harmonic analysis |
| topic | Mathematics Harmonic analysis Fourier analysis Abstract Harmonic Analysis Fourier Analysis Theoretical, Mathematical and Computational Physics Mathematik Harmonische Analyse (DE-588)4023453-8 gnd Unsicherheit (DE-588)4186957-6 gnd Unschärfe (DE-588)4273405-8 gnd Unschärferelation (DE-588)4186953-9 gnd |
| topic_facet | Mathematics Harmonic analysis Fourier analysis Abstract Harmonic Analysis Fourier Analysis Theoretical, Mathematical and Computational Physics Mathematik Harmonische Analyse Unsicherheit Unschärfe Unschärferelation |
| url | https://doi.org/10.1007/978-3-642-78377-7 |
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