On infinitely smooth almost-wavelets with compact support.

M. Berkolaiko; I. Novikov

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Displaying similar documents to “On infinitely smooth almost-wavelets with compact support.”

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.

On the convergence of the wavelet-Galerkin method for nonlinear filtering

Łukasz D. Nowak, Monika Pasławska-Południak, Krystyna Twardowska (2010)

International Journal of Applied Mathematics and Computer Science

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The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on convergence and its rate. The method is numerically much more efficient than the classical...

Connectivity, homotopy degree, and other properties of α-localized wavelets on R.

Gustavo Garrigós (1999)

Publicacions Matemàtiques

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In this paper, we study general properties of α-localized wavelets and multiresolution analyses, when 1/2 < α ≤ ∞. Related to the latter, we improve a well-known result of A. Cohen by showing that the correspondence m → φ' = Π m(2 ·), between low-pass filters in H(T) and Fourier transforms of α-localized scaling functions (in H(R)), is actually a homeomorphism of topological spaces. We also show that the space of such filters can be regarded as a connected infinite...

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...

Characterizations of Gabor Systems via the Fourier transform.

Wojciech Czaja (2000)

Collectanea Mathematica

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We give characterizations of orthogonal families, tight frames and orthonormal bases of Gabor systems. The conditions we propose are stated in terms of equations for the Fourier transforms of the Gabor system's generating functions.

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.

The wavelet characterization of the space Weak H¹

Heping Liu (1992)

Studia Mathematica

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The space Weak H¹ was introduced and investigated by Fefferman and Soria. In this paper we characterize it in terms of wavelets. Equivalence of four conditions is proved.

Translational averaging for completeness, characterization and oversampling of wavelets.

Richard S. Laugesen (2002)

Collectanea Mathematica

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The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding,...

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...

Non-separable bidimensional wavelet bases.

Albert Cohen, Ingrid Daubechies (1993)

Revista Matemática Iberoamericana

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We build orthonormal and biorthogonal wavelet bases of L(R) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single compactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity...