Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup
نویسندگان
چکیده
In the past decade research on the multiresolution analysis has made considerable progress due to its wide applications. For the basic theory of multiresolution we refer readers to the work in 1, 2 . Recently, we find that a lot of authors try to extend the theory of wavelets on the Euclidean space to nilpotent Lie groups see 3–6 . In this paper we will give the definition of acceptable dilations on the Laguerre hypergroup. The multiresolution analysis on the Laguerre hypergroup K 0, ∞ × R is also defined. Moreover the properties of Haar wavelet bases for La K are investigated. We will prove the results analogous to those on R in 2 , on H in 6 , and on H1 ×H1 × · · · ×H1 in 7 . Let dma x, t be the positive measure defined on K, for a ≥ 0, by
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