Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau's Coherent States, Wavelets and Their Generalizations PDF

By Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau

ISBN-10: 1461212588

ISBN-13: 9781461212584

ISBN-10: 1461270650

ISBN-13: 9781461270652

This ebook provides a survey of the idea of coherent states, wavelets, and a few in their generalizations, emphasizing mathematical buildings. the viewpoint is that either the theories of either wavelets and coherent states may be subsumed right into a unmarried analytic constitution. ranging from the normal concept of coherent states over Lie teams, the authors generalize the formalism via associating coherent states to team representations which are sq. integrable over a homogeneous area; an extra step permits one to dispense with the gang context altogether. during this context, wavelets might be generated from coherent states of the affine team of the genuine line, and higher-dimensional wavelets come up from coherent states of different teams. The unified history makes obvious differently vague homes of wavelets and of coherent states. Many concrete examples, comparable to semisimple Lie teams, the relativity workforce, and several other sorts of wavelets, are mentioned intimately. The publication concludes with actual purposes, centering at the quantum dimension challenge and the quantum-classical transition. meant as an advent to present learn for graduate scholars and others coming into the sphere, the mathematical dialogue is self- contained. With its huge references to the examine literature, the e-book can also be an invaluable compendium of modern effects for physicists and mathematicians already lively within the box.

Show description

Read Online or Download Coherent States, Wavelets and Their Generalizations PDF

Similar waves & wave mechanics books

Download PDF by Paul C. Fife: Dynamics of internal layers and diffusive interfaces

Interfacial phenomena are ordinary in physics, chemistry, biology, and in a number of disciplines bridging those fields. They ensue at any time when a continuum is current that could exist in at the very least assorted chemical or actual "states", and there's a few mechanism which generates or enforces a spatial separation among those states.

Read e-book online Distributed Feedback Laser Diodes and Optical Tunable PDF

Advances in optical fibre dependent communications platforms have performed a very important position within the improvement of the data road. by means of supplying a unmarried mode oscillation and slim spectral output, dispensed suggestions (DFB) semiconductor laser diodes provide first-class optical mild assets in addition to optical filters for fibre established communications and dense wavelength department multiplexing (DWDM) structures.

Read e-book online Satellite Communications PDF

This moment version of satellite tv for pc Communications is a revised, up to date, and more suitable model of the 1st variation (Van Nostrand, 1984) and has been prolonged to incorporate many more moderen themes which are swiftly turning into vital in modem and next-generation satellite tv for pc platforms. the 1st 1/2 the e-book back covers the fundamentals of satellite tv for pc hyperlinks, yet has been up to date to incorporate extra parts comparable to worldwide Positioning and deep area satellites, twin polarization, a number of beaming, complex satellite tv for pc electronics, frequency synthesizers, and electronic frequency turbines.

Lectures on Quantum Gravity by Andres Gomberoff, Donald Marolf PDF

The 2002 Pan-American complicated reports Institute tuition on Quantum Gravity used to be held on the Centro de Estudios Cientificos (CECS),Valdivia, Chile, January 4-14, 2002. the college featured lectures by means of ten audio system, and used to be attended via approximately 70 scholars from over 14 international locations. a first-rate target was once to foster interplay and communique among contributors from various cultures, either within the layman’s feel of the time period and when it comes to ways to quantum gravity.

Extra info for Coherent States, Wavelets and Their Generalizations

Example text

All group spaces and parameter spaces for defining CS will be of this type. ) The Borel sets 8(X) of X consist of elements of the O'-algebra formed by its open sets. + U {oo} satisfying the following properties. 1. 1) IJ(0) = O. 2. 3) iEJ If, in addition, IJ satisfies sup IJ(~) = O~A, 0 = compact then it is called a regular Borel measure. Unless the contrary is stated, all Borel measures will be assumed to be regular. The measure IJ is said to be bounded or finite if IJ(X) < 00. While referring to a measure IJ, we shall use either of the two notations, IJ or dIJ.

Canonical Coherent States Hilbert spaces. This will be dealt with in Chapter 5, and it will also take us into the theory of frames in Chapters 7 and 16. ) To bring out some complex analytic properties of the canonical CS, let ¢ E iJ be an arbitrary vector. ] (nl¢) zn 2 n=O v'n1 (zl¢) exp [J~2] J(z). 60) Here J is an analytic function of the complex variable z. 35) as dv(q,p) = dZAdZ 2. 61) 7rZ and let us define the new measure _ 2 dJL(z, z) = exp [-Izl] dz A dZ 2. 62) . In this notation, "A" denotes the exterior product of the two differentials dz and az (considered as one-forms on the complex manifold C).

L¢ above is bounded. In particular, the POV measure is said to be normalized if a(X) = I (= identity operator on S)). , for each x E X, F(x) is a bounded, positive operator, and, for arbitrary ¢,1jJ E S), the complex function x I-t (¢IF(x)1jJ) is measurable in B(X) [that is, the inverse image of any Borel subset of C belongs to B(X)]. Using F and the regular Borel measure v, we may define the regular POV measure a, such that for all ~ E B(X), a(~) = i F(x) dv(x). 7) The operator function F is then called a density for the POV measure a.

Download PDF sample

Coherent States, Wavelets and Their Generalizations by Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau


by Jason
4.1

Rated 4.48 of 5 – based on 41 votes