Two-wavelet constants for square integrable representations of G/H

Document Type: Research Paper

Authors

1 Department of Mathematics, Center of Excellency in Analysis on Algebraic Structures(CEAAS), Ferdowsi University Of Mashhad, Mashhad, Islamic Republic of Iran.

2 Department of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, Islamic Republic of Iran.

3 Department of Mathematics, Ferdowsi University Of Mashhad, Mashhad, Islamic Republic of Iran.

Abstract

In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations for square integrable representations of homogeneous spaces which give rise to the existence of a unique self adjoint positive operator on the set of admissible wavelets. Finally, we show that this operator is a constant multiple of identity operator when G is a semidirect product group of a unimodular subgroup K and a closed subgroup H.

Keywords


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