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The Resource Analysis in integer and fractional dimensions, Ron Blei

Analysis in integer and fractional dimensions, Ron Blei

Label
Analysis in integer and fractional dimensions
Title
Analysis in integer and fractional dimensions
Statement of responsibility
Ron Blei
Title variation
Analysis in Integer & Fractional Dimensions
Creator
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
UkCbUP
http://library.link/vocab/creatorName
Blei, R. C.
Dewey number
515/.2433
Index
index present
LC call number
QA403
LC item number
.B54 2001
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Cambridge studies in advanced mathematics
Series volume
71
http://library.link/vocab/subjectName
  • Harmonic analysis
  • Functional analysis
  • Probabilities
  • Inequalities (Mathematics)
Label
Analysis in integer and fractional dimensions, Ron Blei
Instantiates
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
CR9780511543012
Extent
1 online resource (xix, 556 pages)
Form of item
online
Isbn
9780521650847
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
Label
Analysis in integer and fractional dimensions, Ron Blei
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
CR9780511543012
Extent
1 online resource (xix, 556 pages)
Form of item
online
Isbn
9780521650847
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote

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