Analysis in integer and fractional dimensions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2001
|
| Series: | Cambridge studies in advanced mathematics
71 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Includes bibliographical references (pages 534-545) and index 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 |
| Physical Description: | 1 Online-Ressource (xix, 556 pages) |
| ISBN: | 0511012667 0511036973 0511543018 0521650844 9780511012662 9780511036972 9780511543012 9780521650847 |
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| id | DE-604.BV043131705 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:25Z |
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| spelling | Blei, R. C., (Ron C.) Verfasser aut Analysis in integer and fractional dimensions Ron Blei Cambridge Cambridge University Press 2001 1 Online-Ressource (xix, 556 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 71 Includes bibliographical references (pages 534-545) and index 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 Analyse harmonique Analyse fonctionnelle Probabilités Inégalités (Mathématiques) MATHEMATICS / Infinity bisacsh Analyse harmonique ram Analyse fonctionnelle ram Probabilités ram Inégalités (mathématiques) ram Functional analysis fast Harmonic analysis fast Inequalities (Mathematics) fast Probabilities fast 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 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=73002 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blei, R. C., (Ron C.) Analysis in integer and fractional dimensions Analyse harmonique Analyse fonctionnelle Probabilités Inégalités (Mathématiques) MATHEMATICS / Infinity bisacsh Analyse harmonique ram Analyse fonctionnelle ram Probabilités ram Inégalités (mathématiques) ram Functional analysis fast Harmonic analysis fast Inequalities (Mathematics) fast Probabilities fast 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_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 | Analyse harmonique Analyse fonctionnelle Probabilités Inégalités (Mathématiques) MATHEMATICS / Infinity bisacsh Analyse harmonique ram Analyse fonctionnelle ram Probabilités ram Inégalités (mathématiques) ram Functional analysis fast Harmonic analysis fast Inequalities (Mathematics) fast Probabilities fast 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 | Analyse harmonique Analyse fonctionnelle Probabilités Inégalités (Mathématiques) MATHEMATICS / Infinity Inégalités (mathématiques) Functional analysis Harmonic analysis Inequalities (Mathematics) Probabilities Harmonische Analyse Ungleichung Funktionalanalysis Wahrscheinlichkeitstheorie |
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