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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
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 ≤ ∞.
2
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Some eigenvalue estimates for wavelet related Toeplitz operators

100%
Nowak K.
Colloquium Mathematicum
|
1993
|
tom 65
|
nr 1
149-156
EN
By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end of the second section we include some comments about the range of applicability of our estimates.
3
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Commutators based on the Calderón reproducing formula

100%
Nowak K.
Studia Mathematica
|
1993
|
tom 104
|
nr 3
285-306
EN
We prove the Schatten-Lorentz ideal criteria for commutators of multiplications and projections based on the Calderón reproducing formula and the decomposition theorem for the space of symbols corresponding to commutators in the Schatten ideal.
4
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Certain function spaces related to the metaplectic representation

100%
Nowak K.
Colloquium Mathematicum
|
1998
|
tom 76
|
nr 1
143-152
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