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Coherent States, Wavelets, and Their Generalizations
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
Two-Dimensional Wavelets and their Relatives
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
Continuous Frames in Hilbert Space
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
Canonical Coherent States
This chapter is devoted to a fairly detailed examination of the quintessential example of coherent states — the canonical coherent states of Schrodinger transition from quantum to classical mechanics.
Quantization, Coherent States, and Complex Structures
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
Quantum frames, quantization and dequantization
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
Discrete Wavelet Transforms
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
Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
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
Wavelets on Manifolds
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