Abstract
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed.
Highlights
As usual, let 0, be the positive half-line, 0,1, 2, be the set of all nonnegative integers, and let 1, 2, be the set of all positive integers.The first examples of orthogonal wavelets on related to the Walsh functions and the corresponding wavelets on the Cantor dyadic group have been constructed in [1]; in [2] and [3], a multifractal structure of this wavelets is observed and conditions for wavelets to generate an unconditional basis in Lq -spaces for all 1 q have been found
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line
These investigations are continued in [4,5,6,7,8,9,10] where among other subjects the algorithms to construct orthogonal and biorthogonal wavelets associated with the generalized Walsh functions are studied
Summary
Let 0, be the positive half-line, 0,1, 2, be the set of all nonnegative integers, and let 1, 2, be the set of all positive integers. The first examples of orthogonal wavelets on related to the Walsh functions and the corresponding wavelets on the Cantor dyadic group have been constructed in [1]; in [2] and [3], a multifractal structure of this wavelets is observed and conditions for wavelets to generate an unconditional basis in Lq -spaces for all 1 q have been found. These investigations are continued in [4,5,6,7,8,9,10] where among other subjects the algorithms to construct orthogonal and biorthogonal wavelets associated with the generalized Walsh functions are studied. Using the notion of an adapted multiresolution analysis suggested by Sendov [12], we discuss an application of the nonstationary dyadic wavelets to compression of the Weierstrass function and the Swartz function
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