Random Fourier Series with Applications to Harmonic Analysis
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A01=Gilles Pisier
A01=Michael B. Marcus
Abelian group
Almost periodic function
Almost surely
Author_Gilles Pisier
Author_Michael B. Marcus
Banach space
Big O notation
Cardinality
Category=PBKF
Central limit theorem
Circle group
Coefficient
Commutative property
Compact group
Compact space
Complex number
Continuous function
Corollary
Discrete group
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivalence class
Existential quantification
Finite group
Fourier series
Gaussian process
Haar measure
Harmonic analysis
Independence (probability theory)
Inequality (mathematics)
Integer
Irreducible representation
Non-abelian
Non-abelian group
Normal distribution
Orthogonal group
Orthogonal matrix
Probability
Probability distribution
Probability measure
Probability space
Random function
Random matrix
Random variable
Rate of convergence
Real number
Ring (mathematics)
Scientific notation
Set (mathematics)
Slepian's lemma
Small number
Smoothness
Stationary process
Subgroup
Subset
Summation
Theorem
Uniform convergence
Unitary matrix
Variance
Product details
- ISBN 9780691082929
- Weight: 227g
- Dimensions: 152 x 229mm
- Publication Date: 21 Nov 1981
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived. The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research.
