Paper's Title:

Szegö Limits and Haar Wavelet Basis

Author(s):

M. N. N. Namboodiri and S. Remadevi

Dept. of Mathematics, Cochin University of Science and Technology,
Cochin-21, Kerala,
India.

nambu@cusat.ac.in

Dept. of Mathematics, College of Engineering,
Cherthala, Kerala,
India.

rema@mec.ac.in
 

Abstract:

This paper deals with Szegö type limits for multiplication operators on L² (R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators T_f using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class of multiplication operators T_f , f∈ L^∞ (R) with respect to Haar (wavelet) system with appropriate ordering. More general classes of orderings of Haar system are identified for which the Szegö type limit exist for certain classes of multiplication operators. Some illustrative examples are also provided.

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