Displaying similar documents to “On a property of continuous solutions of the dilation equation with positive coefficients”

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.

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...

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...

A new technique to estimate the regularity of refinable functions.

Albert Cohen, Ingrid Daubechies (1996)

Revista Matemática Iberoamericana

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We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory to derive numerical estimates for the spectral radius of these operators in certain spaces. This new technique is particularly useful for estimating the regularity in the cases where the refinement equation has an infinite number of nonzero coefficients and in the multidimensional cases. ...

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.

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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.

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...

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...