Localization Operators and Uncertainty Principles for the Hankel Wavelet Transform

The aim of this paper is to prove some uncertainty inequalities for the continuous Hankel wavelet transform, and study the localization operator associated to this transformation.

On the relations of general homogeneous spaces and the two-wavelet localization operators

In this note, the two-wavelet localization operator for square integrable representation of a general homogeneous space is defined. Then among other things, the boundedness properties of this operator is investigated. In particular, it is shown that it is in the Schatten p-class.

Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey-type pseudo-differential operators

We deduce one-parameter group properties for pseudo-differential operators [Formula: see text], where [Formula: see text] belongs to the class [Formula: see text] of certain Gevrey symbols. We use this to show that there are pseudo-differential operators [Formula: see text] and [Formula: see text] which are inverses to each other, where [Formula: see text] and [Formula: see text]. We apply these results to deduce lifting property for modulation spaces and construct explicit isomorphisms between them. For each weight functions [Formula: see text] moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) [Formula: see text] is an isomorphism from [Formula: see text] to [Formula: see text] for every [Formula: see text].