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   -> Volume 3, Issue 4


Preprints: Multiresolution Approximations of Banach Spaces
 
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Vyacheslav L. Zavadsky, Belorussion State Univ.
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PostPosted: Mon Dec 02, 2002 12:50 pm    
Subject: Preprints: Multiresolution Approximations of Banach Spaces
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Preprints: Multiresolution Approximations of Banach Spaces


The following papers are available. Any comments are appreciated.

- 1 -
Title: Multiresolution Approximations of Banach Spaces
Author: Vyacheslav L. Zavadsky

Abstract:
The presented paper is devoted to generalizing of
multiresolution analysis concept on abstract Banach
spaces. Operations specific for the numerical line
(dilation and translation) are changed to suitable abstract
algebraic objects. Some common properties of wavelets are
generalized for the abstract case. This properties are
written in the coefficients terms. Then a sufficient
condition for fast convergence of projections of an element
of the space is written. Main result of the paper: an
estimate of multiresolution approximations error is
obtained.

- 2 -
Title: Wavelet Approximation of Sampled Functions
Author: Vyacheslav L. Zavadsky

Abstract:
The paper is devoted to studying of wavelet approximations
on the base of finite number of samples. The approximated
function is supposed to belong to a Sobolev space. The rate
of convergence is estimated in $L_p[a,b]$. The presented
algorithm give an opportunity to use both uniform and
arbitrary grids. Besides, methods for smoothing of noised
functions are proposed and the corresponding rates of
convergence are estimated.

Vyacheslav L. Zavadsky
Department Of CAD
Belorussion State Univ
FPMI,BGU, Fr. Scaryny Av.,4
220080, Minsk, Belarus
former USSR.
email: Zavadsky%CadCam.BSU.Minsk.By@Relay.USSR.Eu.Net

---
Note from the editor:

These papers can be retrieved by anonymous ftp to
maxwell.math.sc.edu, directory /pub/wavelet/papers/varia,
files zava1.tex (amslatex), zava2.tex (amstex), zava1.ps and zava2.ps
(postscript).
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