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Coherent States, Wavelets, and Their Generalizations

- S. T. Ali, J. Antoine, J. Gazeau
- Mathematics
- 30 October 2013

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now… Expand

Two-Dimensional Wavelets and their Relatives

- J. Antoine, R. Murenzi, P. Vandergheynst, S. T. Ali
- Mathematics
- 23 September 2004

Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms when processing rapidly varying functions and signals. In particular, they offer benefits for real-time… Expand

Continuous Frames in Hilbert Space

- S. T. Ali, J. Antoine, J. Gazeau
- Physics
- 1 February 1993

Abstract The standard theory of frames in Hilbert spaces, using discrete bases, is generalized to one where the basis vectors may be labelled using discrete, continuous, or a mixture of the two types… Expand

Canonical Coherent States

- S. T. Ali, J. Antoine, J. Gazeau
- Computer Science
- 2014

TLDR

Quantization, Coherent States, and Complex Structures

- J. Antoine, S. T. Ali, W. Lisiecki, I. Mladenov, A. Odzijewicz
- Mathematics
- 1995

Quantization, Field Theory, and Representation Theory: On Quantum Mechanics in a Curved Spacetime with Absolute Time (D. Canarutto et al.). Massless Spinning Particles on the Antide Sitter Spacetime… Expand

Two-Dimensional Wavelets and their Relatives: Matrix geometry of wavelet analysis. I

- J. Antoine, R. Murenzi, P. Vandergheynst, S. T. Ali
- Mathematics
- 2004

Quantum frames, quantization and dequantization

- S. T. Ali, J. Antoine
- Mathematics
- 1994

A continuous frame in a Hilbert space is a concept well adapted for constructing very general classes of coherent states, in particular those associated to group representations which are square… Expand

Discrete Wavelet Transforms

- S. T. Ali, J. Antoine, J. Gazeau
- Mathematics
- 2014

This chapter is devoted to discrete wavelets. We start with the standard version, related to multiresolution analysis, and some of its generalizations. Next we extend the analysis to a… Expand

Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames

- S. T. Ali, J. Antoine, J. Gazeau
- Mathematics
- 1991

A connection between a class of positive operator valued measures on a Hilbert space and certain reproducing kernel Hilbert spaces leads to the concept of a reproducing triple. Any such object… Expand

Wavelets on Manifolds

- S. T. Ali, J. Antoine, J. Gazeau
- Physics
- 2014

In this chapter, we discuss the construction of wavelets related to other groups than similitude groups. The first, and most important, case is that of wavelets on the two-sphere… Expand

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