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# Construction of orthonormal multi-wavelets with additional vanishing moments.

Adv. Comput. Math 01/2006; 24:239-262. pp.239-262
Source: DBLP
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##### Article:A Class of Bases in L² for the Sparse Representation of Integral Operators
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ABSTRACT: A class of multi-wavelet bases for L 2 is constructed with the property that a varietyofintegral operators is represented in these bases as sparse matrices, to high precision. In particular, an integral operator K whose kernel is smooth except along a finite number of singular bands has a sparse representation. In addition, the inverse operator (I0K) 01 appearing in the solution of a second-kind integral equation involving K is often sparse in the new bases. The result is an order O(n log 2 n) algorithm for numerical solution of a large class of second-kind integral equations. Key Words. wavelets, integral equations, sparse matrices AMS(MOS) subject classifications. 42C15, 45L10, 65R10, 65R20 Families of functions h a;b , h a;b (x)=jaj 01=2 h / x 0 b a ! ; a; b 2 R;a6=0; derived from a single function h by dilation and translation, which form a basis for L 2 (R), are known as wavelets (Grossman and Morlet [9]). In recentyears, these families have received study by...
07/1999;
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##### Article:Biorthogonal Wavelet Expansions
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ABSTRACT: This paper is concerned with developing conditions on a given finite collection of compactly supported algebraically linearly independent refinable functions that insure the existence of biorthogonal systems of refinable functions with similar properties. In particular, we address the close connection of this issue with stationary subdivision schemes.
Constructive Approximation 10/1997; 13(3):293-328. · 1.12 Impact Factor
• ##### Article:Fractal Functions and Wavelet Expansions Based on Several Scaling Functions
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ABSTRACT: We present a method for constructing translation and dilation invariant functions spaces using fractal functions defined by a certain class of iterated function systems. These spaces generalize the C0 function spaces constructed in [D. Hardin, B. Kessler, and P. R. Massopust, J. Approx. Theory71 (1992), 104-120] including, for instance, arbitrarily smooth function spaces. These new function spaces are generated by several scaling functions and their integer-translates. We give necessary and sufficient conditions for these function spaces to form a multiresolution analysis of L2.
Journal of Approximation Theory.