Fourier integrals in classical analysis:
Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classic...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1993
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| Schriftenreihe: | Cambridge tracts in mathematics
105 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions |
| Beschreibung: | 1 Online-Ressource (x, 236 Seiten) |
| ISBN: | 9780511530029 |
| DOI: | 10.1017/CBO9780511530029 |
Internformat
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| 505 | 8 | |a 5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n] | |
| 520 | |a Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions | ||
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Datensatz im Suchindex
| _version_ | 1804176883652231168 |
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| any_adam_object | |
| author | Sogge, Christopher D. 1960- |
| author_GND | (DE-588)104999275X |
| author_facet | Sogge, Christopher D. 1960- |
| author_role | aut |
| author_sort | Sogge, Christopher D. 1960- |
| author_variant | c d s cd cds |
| building | Verbundindex |
| bvnumber | BV043941637 |
| classification_rvk | SK 450 SK 620 |
| collection | ZDB-20-CBO |
| contents | 5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n] |
| ctrlnum | (ZDB-20-CBO)CR9780511530029 (OCoLC)849876839 (DE-599)BVBBV043941637 |
| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511530029 |
| format | Electronic eBook |
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| id | DE-604.BV043941637 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511530029 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350607 |
| oclc_num | 849876839 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (x, 236 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Sogge, Christopher D. 1960- Verfasser (DE-588)104999275X aut Fourier integrals in classical analysis Christopher D. Sogge Cambridge Cambridge University Press 1993 1 Online-Ressource (x, 236 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 105 5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n] Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions Fourier series Fourier integral operators Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Fourier-Integraloperator (DE-588)4155104-7 gnd rswk-swf Fourier-Integral (DE-588)4121290-3 gnd rswk-swf Fourier-Integral (DE-588)4121290-3 s DE-604 Fourier-Integraloperator (DE-588)4155104-7 s Harmonische Analyse (DE-588)4023453-8 s Analysis (DE-588)4001865-9 s Erscheint auch als Druck-Ausgabe 978-0-521-43464-5 Erscheint auch als Druck-Ausgabe 978-0-521-06097-4 https://doi.org/10.1017/CBO9780511530029 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Sogge, Christopher D. 1960- Fourier integrals in classical analysis 5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n] Fourier series Fourier integral operators Harmonische Analyse (DE-588)4023453-8 gnd Analysis (DE-588)4001865-9 gnd Fourier-Integraloperator (DE-588)4155104-7 gnd Fourier-Integral (DE-588)4121290-3 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4001865-9 (DE-588)4155104-7 (DE-588)4121290-3 |
| title | Fourier integrals in classical analysis |
| title_auth | Fourier integrals in classical analysis |
| title_exact_search | Fourier integrals in classical analysis |
| title_full | Fourier integrals in classical analysis Christopher D. Sogge |
| title_fullStr | Fourier integrals in classical analysis Christopher D. Sogge |
| title_full_unstemmed | Fourier integrals in classical analysis Christopher D. Sogge |
| title_short | Fourier integrals in classical analysis |
| title_sort | fourier integrals in classical analysis |
| topic | Fourier series Fourier integral operators Harmonische Analyse (DE-588)4023453-8 gnd Analysis (DE-588)4001865-9 gnd Fourier-Integraloperator (DE-588)4155104-7 gnd Fourier-Integral (DE-588)4121290-3 gnd |
| topic_facet | Fourier series Fourier integral operators Harmonische Analyse Analysis Fourier-Integraloperator Fourier-Integral |
| url | https://doi.org/10.1017/CBO9780511530029 |
| work_keys_str_mv | AT soggechristopherd fourierintegralsinclassicalanalysis |