Topological vector spaces and distributions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, New York
Dover Publications
2012
|
| Edition: | This Dover edition , first published in 2012, is a corrected, unabridged republication of the work originally published in 1966 by the Addison-Wesley Publishing Company, Reading, Massachusetts |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 449 Seiten |
| ISBN: | 9780486488509 0486488500 |
Staff View
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Record in the Search Index
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| adam_text | Contents Terminology and Notations Chapter 1 Banach Spaces 1. 2. 3. 4. 5. 6. 7. 8. 9. The definition of Banach spaces......................................................... 5 Some notions from algebra and topology.............................................. 17 Subspaces.................................................................................................. 27 Linear maps.................................................................................................. 35 Linear forms.................................................................................................. 40 The Hahn-Banach theorem........................................................................... 45 The dual space............................................................................................ 52 The Banach-Steinhaus theorem............................................................... 62 Banach’s homomorphism theorem andthe closed-graph theorem . . 68 Chapter 2 Locally Convex Spaces 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Some notions from topology..................................................................... 71 Filters........................................................................................................75 Topological vector spaces...........................................................................79 Locally convex spaces................................................................................ 84 Linear maps, subspaces, quotient spaces.................................................... 97 Bounded sets, normability,
metrizability............................................ 108 Products and direct sums......................................................................... 117 Convergence of filters............................................................................... 124 Completeness.......................................................................................... 128 Finite-dimensional and locallycompactspaces......................................... 141 Initial topologies.................................................................................... 149 Final topologies.......................................................................................... 157 xi
xii CONTENTS Chapter З Duality 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. The Hahn-Banach theorem.......................................................................... 176 Pairings...................................................................................................... 183 Polarity...................................................................................................... 190 ©-topologies............................................ 195 The Mackey topology............................................................................... 203 Barrelled spaces........................................................................................... 211 Bornological spaces..................................................................................... 220 Reflexivity................................................................................................ 226 Montei spaces...........................................................................................231 The Banach-Dieudonné theorem.............................................................. 243 Grothendieck’s completeness theorem.................................................. 247 The transpose of a linear map....................................................................254 Duals of subspaces and quotientspaces.................................................... 260 Duals of products and direct sums........................................................ 266 Schwartz
spaces.......................................................................................... 271 Distinguished spaces............................................................................... 288 The homomorphism theorem and the closed-graph theorem . . . 294 Chapter 4 Distributions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. The definition of distributions....................................................................313 Support...................................................................................................... 317 Derivation................................................................................................ 323 Distributions of finite order................................................................... 337 Integrable distributions......................................................................... 344 Multiplication.......................................................................................... 347 Bilinear maps.......................................................................................... 355 Tensor product.......................................................................................... 365 Convolution................................................................................................ 381 Regularization.......................................................................................... 401 Fourier transform.................................................................................... 408 Bibliography
........................................................................................... 427 Index of notations................................................................................ 437 Tables....................................................................................................... 441 Index.............................................................................................................443
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| adam_txt |
Contents Terminology and Notations Chapter 1 Banach Spaces 1. 2. 3. 4. 5. 6. 7. 8. 9. The definition of Banach spaces. 5 Some notions from algebra and topology. 17 Subspaces. 27 Linear maps. 35 Linear forms. 40 The Hahn-Banach theorem. 45 The dual space. 52 The Banach-Steinhaus theorem. 62 Banach’s homomorphism theorem andthe closed-graph theorem . . 68 Chapter 2 Locally Convex Spaces 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Some notions from topology. 71 Filters.75 Topological vector spaces.79 Locally convex spaces. 84 Linear maps, subspaces, quotient spaces. 97 Bounded sets, normability,
metrizability. 108 Products and direct sums. 117 Convergence of filters. 124 Completeness. 128 Finite-dimensional and locallycompactspaces. 141 Initial topologies. 149 Final topologies. 157 xi
xii CONTENTS Chapter З Duality 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. The Hahn-Banach theorem. 176 Pairings. 183 Polarity. 190 ©-topologies. 195 The Mackey topology. 203 Barrelled spaces. 211 Bornological spaces. 220 Reflexivity. 226 Montei spaces.231 The Banach-Dieudonné theorem. 243 Grothendieck’s completeness theorem. 247 The transpose of a linear map.254 Duals of subspaces and quotientspaces. 260 Duals of products and direct sums. 266 Schwartz
spaces. 271 Distinguished spaces. 288 The homomorphism theorem and the closed-graph theorem . . . 294 Chapter 4 Distributions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. The definition of distributions.313 Support. 317 Derivation. 323 Distributions of finite order. 337 Integrable distributions. 344 Multiplication. 347 Bilinear maps. 355 Tensor product. 365 Convolution. 381 Regularization. 401 Fourier transform. 408 Bibliography
. 427 Index of notations. 437 Tables. 441 Index.443 |
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| author | Horváth, Juan 1924- |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | This Dover edition , first published in 2012, is a corrected, unabridged republication of the work originally published in 1966 by the Addison-Wesley Publishing Company, Reading, Massachusetts |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T17:22:25Z |
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| institution | BVB |
| isbn | 9780486488509 0486488500 |
| language | English |
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| physical | xii, 449 Seiten |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Dover Publications |
| record_format | marc |
| spelling | Horváth, Juan 1924- Verfasser (DE-588)140510281 aut Topological vector spaces and distributions John Horváth, Professor emeritus of Mathematis, University of Maryland This Dover edition , first published in 2012, is a corrected, unabridged republication of the work originally published in 1966 by the Addison-Wesley Publishing Company, Reading, Massachusetts Mineola, New York Dover Publications 2012 © 1966, 1994 xii, 449 Seiten txt rdacontent n rdamedia nc rdacarrier Topologischer Vektorraum (DE-588)4122383-4 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 s Topologischer Vektorraum (DE-588)4122383-4 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032700992&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Horváth, Juan 1924- Topological vector spaces and distributions Topologischer Vektorraum (DE-588)4122383-4 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| subject_GND | (DE-588)4122383-4 (DE-588)4070505-5 |
| title | Topological vector spaces and distributions |
| title_auth | Topological vector spaces and distributions |
| title_exact_search | Topological vector spaces and distributions |
| title_exact_search_txtP | Topological vector spaces and distributions |
| title_full | Topological vector spaces and distributions John Horváth, Professor emeritus of Mathematis, University of Maryland |
| title_fullStr | Topological vector spaces and distributions John Horváth, Professor emeritus of Mathematis, University of Maryland |
| title_full_unstemmed | Topological vector spaces and distributions John Horváth, Professor emeritus of Mathematis, University of Maryland |
| title_short | Topological vector spaces and distributions |
| title_sort | topological vector spaces and distributions |
| topic | Topologischer Vektorraum (DE-588)4122383-4 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| topic_facet | Topologischer Vektorraum Distribution Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032700992&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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