Displaying similar documents to “Construction of functions with prescribed Hölder and chirp exponents.”

Non-separable bidimensional wavelet bases.

Albert Cohen, Ingrid Daubechies (1993)

Revista Matemática Iberoamericana

Similarity:

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...

A scale-space approach with wavelets to singularity estimation

Jérémie Bigot (2005)

ESAIM: Probability and Statistics

Similarity:

This paper is concerned with the problem of determining the typical features of a curve when it is observed with noise. It has been shown that one can characterize the Lipschitz singularities of a signal by following the propagation across scales of the modulus maxima of its continuous wavelet transform. A nonparametric approach, based on appropriate thresholding of the empirical wavelet coefficients, is proposed to estimate the wavelet maxima of a signal observed with noise at various...

Pointwise smoothness, two-microlocalization and wavelet coefficients.

Stéphane Jaffard (1991)

Publicacions Matemàtiques

Similarity:

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...

Dimension functions, scaling sequences, and wavelet sets

Arambašić Ljiljana, Damir Bakić, Rajna Rajić (2010)

Studia Mathematica

Similarity:

The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function D there exists an MSF wavelet whose dimension function coincides with D. Our method...

Wavelet techniques for pointwise regularity

Stéphane Jaffard (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

Let E be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with E , and denoted by C E α ( x 0 ) . We show how properties of E are transferred into properties of C E α ( x 0 ) . Applications are given in multifractal analysis.

The wavelet type systems

Barbara Wolnik (2006)

Banach Center Publications

Similarity:

We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

Similarity:

After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

Wavelets obtained by continuous deformations of the Haar wavelet.

Aline Bonami, Sylvain Durand, Guido Weiss (1996)

Revista Matemática Iberoamericana

Similarity:

One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular,...

Wavelets on the integers.

Philip Gressman (2001)

Collectanea Mathematica

Similarity:

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...

Construction of Non-MSF Non-MRA Wavelets for L²(ℝ) and H²(ℝ) from MSF Wavelets

Aparna Vyas (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].