A note on wavelet subspaces

Hutník, Ondrej

doi:10.1007/s00605-008-0084-9

Cited by 16 publications

(22 citation statements)

References 7 publications

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“…Let us mention that by taking a system of admissible wavelets ψ n forming all together an orthonormal basis of L 2 (R) one gets a full decomposition of the space L 2 (G, dν). We also mention the paper [10] where the above construction is applied for the specific wavelets on R and wavelet subspaces are studied in more detail therein. An orthogonal decomposition of admissible wavelets is also constructed e.g.…”

Section: Ondrej Hutník Ieotmentioning

confidence: 99%

On Toeplitz-type Operators Related to Wavelets

Hutník

2008

Integr. equ. oper. theory

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Let G be the "ax + b"-group with the left invariant Haar measure dν and ψ be a fixed real-valued admissible wavelet on L2(R). The structure of the space of Calderón (wavelet) transforms W ψ (L2(R)) inside L2(G, dν) is described. Using this result some representations, properties and the Wick calculus of the Calderón-Toeplitz operators Ta acting on W ψ (L2(R)) whose symbols a = a(ζ) depend on v = ζ for ζ ∈ G are investigated. (2000). Primary 46E22, 47B35; Secondary 42C40. Mathematics Subject Classification

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Section: Ondrej Hutník Ieotmentioning

confidence: 99%

On Toeplitz-type Operators Related to Wavelets

Hutník

2008

Integr. equ. oper. theory

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“…In [8] we have proved the following important result describing the structure of wavelet subspaces A (k) inside L 2 (G, dν).…”

Section: Preliminariesmentioning

confidence: 92%

On Boundedness of Calderón–Toeplitz Operators

Hutník

2011

Integr. Equ. Oper. Theory

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We study the boundedness of Toeplitz-type operators defined in the context of the Calderón reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for simultaneous boundedness of these Calderón-Toeplitz operators on each wavelet subspace for unbounded symbols are given, where investigating the behavior of certain sequence of iterated integrals of symbols is helpful. A number of examples and counterexamples is given.Mathematics Subject Classification (2010). Primary 47B35, 42C40; Secondary 47G30, 47L80.

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“…See the papers [2][3][4]9]. It has also been motivated by the study of spaces of wavelet transform using restriction principles [11,12]. In the short note [1] we have constructed discrete versions (frames) of our wavelet transforms.…”

Section: Forerunnersmentioning

confidence: 99%

“…The proof consists of writing the wavelet transform (4.6) as a composition of several unitary operators and is suggested by the techniques used in [12,14]. We need to introduce two auxiliary operators.…”

Section: Definitionmentioning

confidence: 99%

Super-Wavelets Versus Poly-Bergman Spaces

Abreu

2012

Integr. Equ. Oper. Theory

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We investigate a vector-valued version of the classical continuous wavelet transform. Special attention is given to the case when the analyzing vector consists of the first elements of the basis of admissible functions, namely the functions whose Fourier transform is a Laguerre function. In this case, the resulting spaces are, up to a multiplier isomorphism, poly-Bergman spaces. To demonstrate this fact, we introduce a new map and call it the polyanalytic Bergman transform. Our method of proof uses Vasilevski's restriction principle for Bergman-type spaces. The construction is based on the idea of multiplexing of signals.Mathematics Subject Classification (2010). Primary 47B32; Secondary 94A12.

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A note on wavelet subspaces

Cited by 16 publications

References 7 publications

On Toeplitz-type Operators Related to Wavelets

On Toeplitz-type Operators Related to Wavelets

On Boundedness of Calderón–Toeplitz Operators

Super-Wavelets Versus Poly-Bergman Spaces

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