Reproducing kernels and time-frequency localization operators

Abstract

This paper gives a series of isometric injective operators

and

by using the wavelet transform and the Cayley transform from upper-half plane U to unit disc B, and shows that

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 _α and T _α ⁻, and gives eigenvalues and eigenfunctions of a class of special localization operators which extends the results of Daubechies in [4].

Keywords:

• Hilbert space
• Reporducing kernel
• Localization operator
• Wavelet transform
• Cayley transform
• Affine group

AMS:

• 47B38
• 47G10
• 47A25

^∗Corresponding author

^∗Corresponding author

Notes

^∗Corresponding author

Additional information

Notes on contributors

Lizhong peng