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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…
Image analysis with two-dimensional continuous wavelet transform
- J. Antoine, P. Carrette, R. Murenzi, B. Piette
- Computer Science, MathematicsSignal Process.
- 1 April 1993
This work discusses the general properties of the CWT and applies it, both analytically and graphically, to a number of simple geometrical objects: a line, a square, an angle, etc.
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…
Partial *- Algebras and Their Operator Realizations
Foreword. Introduction. I: Theory of Partial O*-Algebras. 1. Unbounded Linear Operators in Hilbert Spaces. 2. Partial O*-Algebras. 3.Commutative Partial O*-Algebras. 4. Topologies on Partial…
Temporally stable coherent states for infinite well and Poschl-Teller potentials
This article is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite…
Wavelets on the 2-sphere: A group-theoretical approach
We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S-2, based on the construction of general coherent states associated to square integrable…
Two-dimensional directional wavelets and the scale-angle representation
This work shows how the reproducing kernel may be used for defining and evaluating the scale and angle-resolving power of a wavelet, and illustrates the usefulness of the scale-angle representation of the CWT on the problem of disentangling a train of damped plane waves.
Coherent states and their generalizations - A mathematical overview
We present a survey of the theory of coherent states (CS); and some of their generalizations, with emphasis on the mathematical structure, rather than on physical applications. Starting from the…
Wavelets on the sphere: implementation and approximations
We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional…