Displaying similar documents to “A new technique to estimate the regularity of refinable functions.”

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...

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.

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.

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 infinitely smooth almost-wavelets with compact support.

M. Berkolaiko, I. Novikov (1993)

Collectanea Mathematica

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There are known wavelets with exponential decay on infinity [2,3,4] and wavelets with compact support [5]. But these functions have finite smoothness. It is known that there do not exist infinitely differentiable compactly supported wavelets.

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.

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...