Eigenfunction wavelet transform

Abstract

Translation and convolution for eigenfunction transform studied by Zemanian [A.H. Zemanian, Ortho-normal series expansions of certain distributions and distributional transform calculus, J. Math. Anal. Appl. 14 (1966), pp. 1255-1265; A.H. Zemanian, Generalized Integral Transformations, Interscience Publishers, New York, 1968.] are defined. These operators are used to define eigenfunction wavelet transform. Certain boundedness, continuity results and inversion formulae for the continuous eigenfunction wavelet transform are obtained. Important properties of the discrete eigenfunction wavelet transform are given. © 2009 Taylor & Francis.