Analysis in integer and fractional dimensions:
This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial mea...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
71 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xix, 556 Seiten) |
| ISBN: | 9780511543012 |
| DOI: | 10.1017/CBO9780511543012 |
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| 505 | 8 | |a Part I: A prologue: mostly historical -- Part II: Three classical inequalities -- Part III: A fourth inequality -- Part IV: Elementary properties of the Frechet variation- an introduction to tensor products -- Part V: The Grothendieck factorization theorem -- Part VI: An introduction to multidimensional measure theory -- Part VII: An introduction to harmonic analysis -- Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability) -- Part IX: Product Fréchet measures -- Part X: Brownian motion and the Wiener process -- Part XI: Integrators -- Part XII: A '3/2-dimensional' Cartesian product -- Part XIII: Fractional cartesian products and cominatorial dimension -- Part XIV: The last chapter: leads and loose ends | |
| 520 | |a This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Blei, Ron |
| author_GND | (DE-588)106993707X |
| author_facet | Blei, Ron |
| author_role | aut |
| author_sort | Blei, Ron |
| author_variant | r b rb |
| building | Verbundindex |
| bvnumber | BV043942214 |
| classification_rvk | SK 450 |
| collection | ZDB-20-CBO |
| contents | Part I: A prologue: mostly historical -- Part II: Three classical inequalities -- Part III: A fourth inequality -- Part IV: Elementary properties of the Frechet variation- an introduction to tensor products -- Part V: The Grothendieck factorization theorem -- Part VI: An introduction to multidimensional measure theory -- Part VII: An introduction to harmonic analysis -- Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability) -- Part IX: Product Fréchet measures -- Part X: Brownian motion and the Wiener process -- Part XI: Integrators -- Part XII: A '3/2-dimensional' Cartesian product -- Part XIII: Fractional cartesian products and cominatorial dimension -- Part XIV: The last chapter: leads and loose ends |
| ctrlnum | (ZDB-20-CBO)CR9780511543012 (OCoLC)849894457 (DE-599)BVBBV043942214 |
| 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/CBO9780511543012 |
| format | Electronic eBook |
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| id | DE-604.BV043942214 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511543012 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351183 |
| oclc_num | 849894457 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| physical | 1 online resource (xix, 556 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 | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Blei, Ron Verfasser (DE-588)106993707X aut Analysis in integer and fractional dimensions Ron Blei Analysis in Integer & Fractional Dimensions Cambridge Cambridge University Press 2001 1 online resource (xix, 556 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 71 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Part I: A prologue: mostly historical -- Part II: Three classical inequalities -- Part III: A fourth inequality -- Part IV: Elementary properties of the Frechet variation- an introduction to tensor products -- Part V: The Grothendieck factorization theorem -- Part VI: An introduction to multidimensional measure theory -- Part VII: An introduction to harmonic analysis -- Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability) -- Part IX: Product Fréchet measures -- Part X: Brownian motion and the Wiener process -- Part XI: Integrators -- Part XII: A '3/2-dimensional' Cartesian product -- Part XIII: Fractional cartesian products and cominatorial dimension -- Part XIV: The last chapter: leads and loose ends This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists Harmonic analysis Functional analysis Probabilities Inequalities (Mathematics) Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Ungleichung (DE-588)4139098-2 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Funktionalanalysis (DE-588)4018916-8 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Ungleichung (DE-588)4139098-2 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-65084-7 Cambridge studies in advanced mathematics 71 (DE-604)BV044781283 71 https://doi.org/10.1017/CBO9780511543012 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Blei, Ron Analysis in integer and fractional dimensions Cambridge studies in advanced mathematics Part I: A prologue: mostly historical -- Part II: Three classical inequalities -- Part III: A fourth inequality -- Part IV: Elementary properties of the Frechet variation- an introduction to tensor products -- Part V: The Grothendieck factorization theorem -- Part VI: An introduction to multidimensional measure theory -- Part VII: An introduction to harmonic analysis -- Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability) -- Part IX: Product Fréchet measures -- Part X: Brownian motion and the Wiener process -- Part XI: Integrators -- Part XII: A '3/2-dimensional' Cartesian product -- Part XIII: Fractional cartesian products and cominatorial dimension -- Part XIV: The last chapter: leads and loose ends Harmonic analysis Functional analysis Probabilities Inequalities (Mathematics) Harmonische Analyse (DE-588)4023453-8 gnd Ungleichung (DE-588)4139098-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4139098-2 (DE-588)4018916-8 (DE-588)4079013-7 |
| title | Analysis in integer and fractional dimensions |
| title_alt | Analysis in Integer & Fractional Dimensions |
| title_auth | Analysis in integer and fractional dimensions |
| title_exact_search | Analysis in integer and fractional dimensions |
| title_full | Analysis in integer and fractional dimensions Ron Blei |
| title_fullStr | Analysis in integer and fractional dimensions Ron Blei |
| title_full_unstemmed | Analysis in integer and fractional dimensions Ron Blei |
| title_short | Analysis in integer and fractional dimensions |
| title_sort | analysis in integer and fractional dimensions |
| topic | Harmonic analysis Functional analysis Probabilities Inequalities (Mathematics) Harmonische Analyse (DE-588)4023453-8 gnd Ungleichung (DE-588)4139098-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Harmonic analysis Functional analysis Probabilities Inequalities (Mathematics) Harmonische Analyse Ungleichung Funktionalanalysis Wahrscheinlichkeitstheorie |
| url | https://doi.org/10.1017/CBO9780511543012 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT bleiron analysisinintegerandfractionaldimensions AT bleiron analysisinintegerfractionaldimensions |