Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 4 (2009), 239 -- 252


S. K. Upadhyay, R. N. Yadav and Lokenath Debnath

Abstract. In this paper the wavelet transformation on Gelfand and Shilov spaces of type WM(⬛n), WΩn) and WMΩn) is studied. It is shown that Wψφ : WM(⬛n) → WM(⬛n×⬛+n), Wψφ : WΩn) → WΩn×⬛+n) and Wψφ : WMΩn) → WMΩn×⬛+n) is linear and continuous where ⬛n and Δn are n-dimensional real numbers and complex numbers. A boundedness result in a generalized Sobolev space is derived.

2000 Mathematics Subject Classification: 42C40; 46F12.
Keywords: Continuous wavelet transformation; Sobolev space; Fourier transformation; W-spaces.

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S. K. Upadhyay R. N. Yadav
Department of Applied Mathematics, Department of Mathematics and Statistics,
I. T. and C I M S, D S T, B. H. U., D. D. U. Gorakhpur University,
Varanasi - 221005, Gorakhpur,
India. India.

Lokenath Debnath
Department of Mathematics,
The University of Texas-Pan American,
1201 West University Drive,
Edinburg, 78539, USA.