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

• Autorzy: Krzysztof Nowak
• Języki publikacji: EN

Abstrakty

EN

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 ≤ ∞.

Słowa kluczowe

EN

singular values; time-frequency localization

Kategorie tematyczne

• 45C05: Eigenvalue problems
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 81R30: Coherent states
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 1
• Strony: 37-64

Daty

wydano

1996

otrzymano

1995-06-08

poprawiono

1996-01-15

Twórcy

autor

Krzysztof Nowak

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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