IJPAM: Volume 75, No. 4 (2012)

ORTHOGONAL VECTOR VALUED WAVELETS ON $\mathbb{R}_{+}$

P. Manchanda$^1$, Vikram Sharma$^2$
$^{1,2}$Department of Mathematics
Guru Nanak Dev University
Amritsar, 143005, INDIA


Abstract. Xia and Suter [15] have introduced the notion of vector valued multiresolution analysis on real line $\mathbb{R}$. Chen and Chang [1] have given an algorithm for construction of vector valued wavelets. Farkov [3] has studied the notion of multiresolution analysis on locally abelian groups and constructed the compactly supported orthogonal p-wavelets on $L^{2}(\mathbb{R}_{+})$. In this paper, we introduce vector valued multiresolution p-analysis on positive half line. We find necessary and sufficient condition for the existence of associated vector valued wavelets. We construct vector valued wavelets on $\mathbb{R}_{+}$. Our approach is connected with Walsh-Fourier theory.

Received: December 6, 2011

AMS Subject Classification: 42A38, 42A55, 42C10, 42C15, 42C40

Key Words and Phrases: multiresolution $p$-analysis, Walsh function, Walsh-Fourier transform, orthogonal vector valued wavelets

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 4