Titlebook: Wavelet Transforms and Localization Operators; M. W. Wong Book 2002 Springer Basel AG 2002 functional analysis.harmonic analysis.mathemati

NORM

ironic

Square-Integrable Representations,We are now well-equipped to study the main contents in this book. We begin with a study of square-integrable representations of locally compact and Hausdorff groups on Hilbert spaces. This chapter can be considered as a continuation of the study of unitary representations begun in Chapter 5.

TIGER

Wavelet Constants,We begin with the following theorem, which is an extension of the resolution of the identity formula given in Theorem 6.1. This extension allows us to obtain some interesting results on the wavelet constants for unimodular groups.

Binge-Drinking

pacific

Compact Groups,We look at left regular representations ... of compact and Haus-dorff groups . in this chapter. Let ϕ ∈ ..(.). Then, using Minkowski’s inequality in integral form, the unimodularity of the group . and Schwarz’ inequality, we get.Thus, every function go in ... with . is an admissible wavelet for the left regular representation ... of .

松软无力

Compact Groups,We look at left regular representations ... of compact and Haus-dorff groups . in this chapter. Let ϕ ∈ ..(.). Then, using Minkowski’s inequality in integral form, the unimodularity of the group . and Schwarz’ inequality, we get.Thus, every function go in ... with . is an admissible wavelet for the left regular representation ... of .

Condense

Trace Class Norm Inequalities,As a sequel to Chapter 13, we prove in this chapter that the constant . in Proposition 13.1 can be improved to . and obtain a lower bound for the norm ‖..‖ .. of the localization operator .. : . → . in .. in terms of the function .. on . defined by.. ∈ ..

善于

Trace Class Norm Inequalities,As a sequel to Chapter 13, we prove in this chapter that the constant . in Proposition 13.1 can be improved to . and obtain a lower bound for the norm ‖..‖ .. of the localization operator .. : . → . in .. in terms of the function .. on . defined by.. ∈ ..

广告

Choreography

The Weyl-Heisenberg Group,We show in this chapter that localization operators on the Weyl-Heisenberg group are the same as the linear operators studied by Daubechies in the paper [12] on signal analysis. We begin with a detailed study of the Weyl-Heisenberg group.