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Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

100%

Nowak K.

Studia Mathematica

1996

tom 119

nr 1

37-64

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions $g ↦ P_{g,ϕ}$, where for a fixed function ϕ, $P_{g,ϕ}$ denotes the one-dimensional orthogonal projection on the function $U_gϕ$, U is a group representation and g is an element of the group. They are defined as integrals $ʃ_W P_{g,ϕ} dg$, where W is an open, relatively compact subset of a group. Our main result is a characterization of function spaces corresponding to local Toeplitz operators with pth power summable eigenvalues, 0 < p ≤ ∞.

Certain function spaces related to the metaplectic representation

70%

Nowak K.

Colloquium Mathematicum

1998

tom 76

nr 1

143-152

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Nowak K.

1 1998

1 1996

Wyniki wyszukiwania

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Certain function spaces related to the metaplectic representation