Analysis of TM scattering from open two-dimensional perfectly conducting shells using aggregated compactly-supported wavelet bases

1996 ◽  
Vol 143 (2) ◽  
pp. 152 ◽  
Author(s):  
V. Jandhyala ◽  
E. Michielssen ◽  
R. Mittra
Keyword(s):  
Two Dimensional ◽  
Wavelet Bases ◽  
Compactly Supported

scholarly journals HAAR BASES FOR $L^2(\mathbb{Q}_2^2)$ GENERATED BY ONE WAVELET FUNCTION

2012 ◽  
Vol 10 (05) ◽  
pp. 1250042 ◽  
Author(s):  
S. ALBEVERIO ◽  
M. SKOPINA
Keyword(s):  
Wavelet Function ◽  
Orthogonal Basis ◽  
Explicit Description ◽  
Two Dimensional ◽  
Wavelet Bases ◽  
The Real

The concept of p-adic quincunx Haar MRA was introduced and studied in Ref. 12. In contrast to the real setting, infinitely many different wavelet bases are generated by a p-adic MRA. We give an explicit description for all wavelet functions corresponding to the quincunx Haar MRA. Each one generates an orthogonal basis, one of them was presented in Ref. 12. A connection between quincunx Haar MRA and two-dimensional separable Haar MRA is also found.

STABILITY OF BIORTHOGONAL WAVELET BASES

2003 ◽  
Vol 01 (01) ◽  
pp. 75-92
Author(s):  
PAUL F. CURRAN ◽  
GARY McDARBY
Keyword(s):  
Linear Operator ◽  
Lifting Scheme ◽  
Simple Eigenvalue ◽  
Single Parameter ◽  
Multiple Eigenvalue ◽  
Scaling Functions ◽  
Biorthogonal Wavelet ◽  
Wavelet Bases ◽  
Compactly Supported

We investigate the lifting scheme as a method for constructing compactly supported biorthogonal scaling functions and wavelets. A well-known issue arising with the use of this scheme is that the resulting functions are only formally biorthogonal. It is not guaranteed that the new wavelet bases actually exist in an acceptable sense. To verify that these bases do exist one must test an associated linear operator to ensure that it has a simple eigenvalue at one and that all its remaining eigenvalues have modulus less than one, a task which becomes numerically intensive if undertaken repeatedly. We simplify this verification procedure in two ways: (i) we show that one need only test an identifiable half of the eigenvalues of the operator, (ii) we show that when the operator depends upon a single parameter, the test first fails for values of that parameter at which the eigenvalue at one becomes a multiple eigenvalue. We propose that this new verification procedure comprises a first step towards determining simple conditions, supplementary to the lifting scheme, to ensure existence of the new wavelets generated by the scheme and develop an algorithm to this effect.

scholarly journals Compactly supported wavelet bases for Sobolev spaces

2003 ◽  
Vol 15 (3) ◽  
pp. 224-241 ◽  
Author(s):  
Rong-Qing Jia ◽  
Jianzhong Wang ◽  
Ding-Xuan Zhou
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Bases ◽  
Compactly Supported

M-CHANNEL MRA AND APPLICATION TO ANISOTROPIC SOBOLEV SPACES

2005 ◽  
Vol 03 (02) ◽  
pp. 153-166
Author(s):  
ELENA CORDERO
Keyword(s):  
Tensor Product ◽  
Sobolev Spaces ◽  
Unit Interval ◽  
Biorthogonal Wavelet ◽  
Bernstein Type ◽  
Wavelet Bases ◽  
Compactly Supported ◽  
Anisotropic Sobolev Spaces ◽  
Dilation Factor ◽  
Bernstein Type Inequalities

In this paper we construct compactly supported biorthogonal wavelet bases of the interval, with dilation factor M. Next, the natural MRA on the cube arising from the tensor product of a multilevel decomposition of the unit interval is developed. New Jackson and Bernstein type inequalities are proved, providing a characterization for anisotropic Sobolev spaces.

scholarly journals Fourier transforms of powers of well-behaved 2D real analytic functions

2018 ◽  
Vol 30 (3) ◽  
pp. 723-732
Author(s):  
Michael Greenblatt
Keyword(s):  
Analytic Functions ◽  
Fourier Transforms ◽  
Newton Polygon ◽  
Companion Paper ◽  
Two Dimensional ◽  
Compactly Supported ◽  
Sharp Estimates ◽  
Real Analytic Functions ◽  
Real Analytic ◽  
Compactly Supported Functions

AbstractThis paper is a companion paper to [6], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [6] are stated in a rather general form. In this paper, we expand on the results of [6] and show that there is a class of “well-behaved” functions that contains a number of relevant examples for which such estimates can be explicitly described in terms of the Newton polygon of the function. We will further see that for a subclass of these functions, one can prove noticeably more precise estimates, again in an explicitly describable way.

scholarly journals M-channel compactly supported biorthogonal cosine-modulated wavelet bases

1998 ◽  
Vol 46 (4) ◽  
pp. 1142-1151 ◽  
Author(s):  
S.C. Chan ◽  
Y. Luo ◽  
K.L. Ho
Keyword(s):  
Wavelet Bases ◽  
Compactly Supported
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