Displaying similar documents to “Closure of dilates of shift-invariant subspaces”

Biorthogonal wavelets, MRA's and shift-invariant spaces

Marcin Bownik, Gustavo Garrigós (2004)

Studia Mathematica

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We give a characterization of biorthogonal wavelets arising from MRA's of multiplicity D entirely in terms of the dimension function. This improves the previous characterization in [8] removing an unnecessary angle condition. Besides we characterize Riesz wavelets arising from MRA's, and present new proofs based on shift-invariant space theory, generalizing the 1-dimensional results appearing in [17].

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...

Calderón's conditions and wavelets.

Ziemowit Rzeszotnik (2001)

Collectanea Mathematica

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The paper presents the proof of the fact that the discrete Calderón condition characterizes the completeness of an orthonormal wavelet basis.

Application of the Haar wavelet method for solution the problems of mathematical calculus

Ü. Lepik, H. Hein (2015)

Waves, Wavelets and Fractals

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In recent times the wavelet methods have obtained a great popularity for solving differential and integral equations. From different wavelet families we consider here the Haar wavelets. Since the Haar wavelets are mathematically most simple to be compared with other wavelets, then interest to them is rapidly increasing and there is a great number of papers,where thesewavelets are used tor solving problems of calculus. An overview of such works can be found in the survey paper by Hariharan...