scholarly journals A Jackson-type inequality associated with wavelet bases decomposition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kai-Cheng Wang
Keyword(s):  
Besov Spaces ◽  
Type Inequality ◽  
Jackson Inequality ◽  
Jackson Type ◽  
Wavelet Coefficients ◽  
Wavelet Bases ◽  
Wavelet Decompositions

AbstractAlthough wavelet decompositions of functions in Besov spaces have been extensively investigated, those involved with mild decay bases are relatively unexplored. In this paper, we study wavelet bases of Besov spaces and the relation between norms and wavelet coefficients. We establish the $l^{p}$ l p -stability as a measure of how effectively the Besov norm of a function is evaluated by its wavelet coefficients and the $L^{p}$ L p -completeness of wavelet bases. We also discuss wavelets with decay conditions and establish the Jackson inequality.

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

BESOV NORMS IN TERMS OF THE CONTINUOUS WAVELET TRANSFORM. APPLICATION TO STRUCTURE FUNCTIONS

1996 ◽  
Vol 06 (05) ◽  
pp. 649-664 ◽  
Author(s):  
VALÉRIE PERRIER ◽  
CLAUDE BASDEVANT
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Besov Spaces ◽  
Inversion Formula ◽  
Structure Functions ◽  
Continuous Wavelet ◽  
Wavelet Coefficients ◽  
Small Scales ◽  
Besov Norms

The continuous wavelet transform is extended to Lp spaces and an inversion formula is demonstrated. From this the Besov spaces can be characterized by the behavior at small scales of the wavelet coefficients. These results apply to the measurement of structure functions.

FORECASTING TIME SERIES USING WAVELETS

2007 ◽  
Vol 05 (05) ◽  
pp. 709-724 ◽  
Author(s):  
MINA AMINGHAFARI ◽  
JEAN-MICHEL POGGI
Keyword(s):  
Time Series ◽  
Prediction Equation ◽  
Stationary Time Series ◽  
Wavelet Coefficients ◽  
Statistical Forecasting ◽  
Stationary Time ◽  
Deterministic Trend ◽  
Wavelet Decompositions ◽  
Direct Regression

This paper deals with wavelets in time series, focusing on statistical forecasting purposes. Recent approaches involve wavelet decompositions in order to handle non-stationary time series in such context. A method, proposed by Renaud et al.,11 estimates directly the prediction equation by direct regression of the process on the Haar non-decimated wavelet coefficients depending on its past values. In this paper, this method is studied and extended in various directions. The new variants are used first for stationary data and after for stationary data contaminated by a deterministic trend.

scholarly journals Multivariate Jackson-type inequality for a new type neural network approximation

2014 ◽  
Vol 38 (24) ◽  
pp. 6031-6037 ◽  
Author(s):  
Shaobo Lin ◽  
Yuanhua Rong ◽  
Zongben Xu
Keyword(s):  
Neural Network ◽  
Type Inequality ◽  
Jackson Type ◽  
New Type

The well-posedness theory for Euler–Poisson fluids with non-zero heat conduction

2014 ◽  
Vol 11 (04) ◽  
pp. 679-703
Author(s):  
Jiang Xu
Keyword(s):  
Heat Conduction ◽  
Besov Spaces ◽  
Hyperbolic Systems ◽  
Type Inequality ◽  
Classical Solutions ◽  
Well Posedness ◽  
Poisson Equations ◽  
The Cauchy Problem ◽  
Critical Besov Spaces ◽  
Temperature Equation

This paper is devoted to the Euler–Poisson equations for fluids with non-zero heat conduction, arising in semiconductor science. Due to the thermal effect of the temperature equation, the local well-posedness theory by Xu and Kawashima (2014) for generally symmetric hyperbolic systems in spatially critical Besov spaces does not directly apply. To deal with this difficulty, we develop a generalized version of the Moser-type inequality by using Bony's decomposition. With a standard iteration argument, we then establish the local well-posedness of classical solutions to the Cauchy problem for intial data in spatially Besov spaces.

Jackson-type inequality on the sphere

2004 ◽  
Vol 102 (1/2) ◽  
pp. 1-36 ◽  
Author(s):  
Zeev Ditzian
Keyword(s):  
Type Inequality ◽  
Jackson Type
Sign in / Sign up

Export Citation Format

Share Document