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[PAST EVENT] The hidden spectrum of Fourier multipliers
November 9, 2012
3pm - 4pm
The algebra of Fourier-Hadamard multipliers on a weighted space L2 (T, w) is considered. A
multiplier is a sequence (?n)n?Z such that the map T : exp(inx)? ?_n exp(inx)
extends to a linear bounded (convolution) operator on the space L2 (T, w). We say that w satis?es the spectral localization property (SLP) if, for every multiplier T, the spectrum of T is the closure of eigenvalues, ?(T) = clos{?n(T)}. We give examples of (A2) weights w satisfying/not satisfying the SLP.
For a class of weights w, all multipliers are described. A historical framework is also discussed, starting from the classical Wiener-Pitt-Schreider phenomenon.
This is a joint project with Igor Verbitsky (Missouri-Columbia).
multiplier is a sequence (?n)n?Z such that the map T : exp(inx)? ?_n exp(inx)
extends to a linear bounded (convolution) operator on the space L2 (T, w). We say that w satis?es the spectral localization property (SLP) if, for every multiplier T, the spectrum of T is the closure of eigenvalues, ?(T) = clos{?n(T)}. We give examples of (A2) weights w satisfying/not satisfying the SLP.
For a class of weights w, all multipliers are described. A historical framework is also discussed, starting from the classical Wiener-Pitt-Schreider phenomenon.
This is a joint project with Igor Verbitsky (Missouri-Columbia).