Analysis in Integer and Fractional Dimensions by Ron Blei
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.-
A Primer of Nonlinear Analysis
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Complex Topological K-Theory
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Mathematical Aspects of Quantum Field Theory
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Enumerative Combinatorics: Volume 1
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Introduction to Homotopy Type Theory
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Hodge Theory and Complex Algebraic Geometry I: Volume 1
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Random Graphs
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Enumerative Combinatorics: Volume 2
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Algebraic Number Theory
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Spectral Theory and Differential Operators
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An Introduction to the Theory of the Riemann Zeta-Function
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Hardy Spaces
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Gaussian Processes on Trees
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Multidimensional Real Analysis I
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Periodic Elliptic Partial Differential Operators
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Higher Index Theory
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A Course in Finite Group Representation Theory
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Optimal Control and Geometry: Integrable Systems
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The Theory of Fusion Systems
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Derived Categories
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Uniform Central Limit Theorems
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Random Fragmentation and Coagulation Processes
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Levy Processes and Stochastic Calculus
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Holomorphic Dynamics
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An Introduction to Invariants and Moduli
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Quasiconformal Surgery in Holomorphic Dynamics
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Martingales in Banach Spaces
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Tolerance Graphs
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An Outline of Ergodic Theory
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Spectra of Discrete Structures
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Analytic Combinatorics in Several Variables
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Fourier Analysis and Partial Differential Equations
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Riemannian Geometry
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Representations of the Infinite Symmetric Group
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Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models
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Local Cohomology
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Multiplicative Number Theory I
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An Introduction to Nonlinear Analysis
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Extremal Graph and Hypergraph Theory
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The Bellman Function Technique in Harmonic Analysis
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Explicit Brauer Induction
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Random Walk: A Modern Introduction
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Clifford Algebras and the Classical Groups
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Wavelets
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The Logarithmic Integral: Volume 2
| SKU | Unavailable |
| ISBN 13 | 9780521650847 |
| ISBN 10 | 0521650844 |
| Title | Analysis in Integer and Fractional Dimensions |
| Author | Ron Blei |
| Series | Cambridge Studies In Advanced Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2001-07-19 |
| Number of pages | 580 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |