Displaying similar documents to “Pointwise smoothness, two-microlocalization and wavelet coefficients.”

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.

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.

On the exact values of coefficients of coiflets

Dana Černá, Václav Finěk, Karel Najzar (2008)

Open Mathematics

Similarity:

In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling...

Non-MSF Wavelets for the Hardy Space H²(ℝ)

Biswaranjan Behera (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.

Wavelets and prediction in time series

Mošová, Vratislava

Similarity:

Wavelets (see [2, 3, 4]) are a recent mathematical tool that is applied in signal processing, numerical mathematics and statistics. The wavelet transform allows to follow data in the frequency as well as time domain, to compute efficiently the wavelet coefficients using fast algorithm, to separate approximations from details. Due to these properties, the wavelet transform is suitable for analyzing and forecasting in time series. In this paper, Box-Jenkins models (see [1, 5]) combined...