Publisher： Taylor & Francis Ltd
ISSN： 0003-6811
Source： Applicable Analysis, Vol.80, Iss.3, 2002-01, pp. : 431-447
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Abstract
This paper gives a series of isometric injective operators $$ eqalign{&T_alpha :H + to L2 left(B, (1 - |z|2 ){alpha - 1}{ dzdbar zoverGamma (alpha )i}right)quad {rm and}cr &T_alpha - :H - to L2 left(B, (1 - |z|2 ){alpha - 1} {dzdbar zover Gamma (alpha )i}right)} $$ by using the wavelet transform and the Cayley transform from upper-half plane U to unit disc B, and shows that $$ T_alpha H + ({rm or } T_alpha - H - ) subseteq L2 left(B, (1 - |z|2 ){alpha - 1} {dzdbar zover Gamma (alpha )i}right) $$ is a reproducing kernel subspace, even Bergman space (or the Conjugate Bergman space). Then it studies the localization operators associated to wavelet transform by using of the operators T
and $ T_alpha - $, and gives eigenvalues and eigenfunctions of a class of special localization operators which extends the results of Daubechies in [4].
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