on a hilbert space of analytic functions and an associated integral transform pdf

On A Hilbert Space Of Analytic Functions And An Associated Integral Transform Pdf

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Bargmann Space Methods in First-Order Optics

In mathematics , the Segal—Bargmann space for Irving Segal and Valentine Bargmann , also known as the Bargmann space or Bargmann—Fock space , is the space of holomorphic functions F in n complex variables satisfying the square-integrability condition:. The space was introduced in the mathematical physics literature separately by Bargmann and Segal in the early s; see Bargmann and Segal Basic information about the material in this section may be found in Folland and Hall It then follows from the Riesz representation theorem that there exists a unique F a in the Segal—Bargmann space such that. The function F a is called the coherent state applied in mathematical physics with parameter a , and the function. Note that.

Bargmann, On a Hilbert space of analytic functions and an associated integral transform

Coherence and Quantum Optics V pp Cite as. Bargmann space techniques in quantum mechanics [1, 2, 3, 4] consist in performing a transformation upon the modes of an harmonic oscillator that renders the modes and the creation and annihilation operators particularly simple. In this paper the Bargmann space techniques are extended to the optical propagation of gaussian beams in a lenslike medium with possible loss or gain [5] yielding a considerably simplified derivation of the algebra of modes and mode generating operators. Unable to display preview. Download preview PDF.

On a Hilbert space of analytic functions and an associated integral transform part I

Scientific Research An Academic Publisher. Berger and L. Fitouhi, M. Hamza and F. Fethi Soltani.

Authors: Muna Tabuni. The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered.

Segal–Bargmann space

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Introduction 0. The problems treated in this paper arose in connection with the attempt to apply the methods of Part I1 to the theory of tempered distributions. In the following we omit the subscript n as long as the dimension n is fixed. The elements of 8 are functions f E 3, and the inner product in 5 is. See [2], hereafter quoted as I or Part I. In the introduction to Part I it was said that Part I1 would deal with harmonic polynomials in 8, and Part I11 with the rotation group.

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