Displaying similar documents to “Commutators based on the Calderón reproducing formula”

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

Krzysztof Nowak (1996)

Studia Mathematica

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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 g ϕ , U is a group representation and g is an element of the group. They are defined as integrals ʃ W P g , ϕ d g , where W is an open,...

Wavelets on the integers.

Philip Gressman (2001)

Collectanea Mathematica

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In this paper the theory of wavelets on the integers is developed. For this, one needs to first find analogs of translations and dyadic dilations which appear in the classical theory. Translations in l2(Z) are defined in the obvious way, taking advantage of the additive group structure of the integers. Dyadic dilations, on the other hand, pose a greater problem. In the classical theory of wavelets on the real line, translation T and dyadic dilation T obey the commutativity relation DT^2...

Pointwise smoothness, two-microlocalization and wavelet coefficients.

Stéphane Jaffard (1991)

Publicacions Matemàtiques

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In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces C , and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet...

Weighted Bergman projections and tangential area integrals

William Cohn (1993)

Studia Mathematica

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Let Ω be a bounded strictly pseudoconvex domain in ℂ n . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection P s f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) .

On the existence of wavelets for non-expansive dilation matrices.

Darrin Speegle (2003)

Collectanea Mathematica

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Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation...

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G. Kyriazis (1998)

Studia Mathematica

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We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces C p α ( ℝ d ) , 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the C p α ( ℝ d ) spaces in terms of the coefficients of wavelet decompositions.

A survey on wavelet methods for (geo) applications.

Willi Freeden, Thorsten Maier, Steffen Zimmermann (2003)

Revista Matemática Complutense

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Wavelets originated in 1980's for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1,+1] and scalar and vector spherical wavelets on the unit sphere 'Omega' are discussed in more detail.