Fourier transforms in generalized Fock spaces. (1990)

• Record Type: Journal Article
• Authors: Schmeelk, John
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 13:Number 3(1990)
• Page Start: 431
• Page End: 441
• Publication Date: 1990
• Subjects: generalized Fock sapces -- tempered distributions -- Fourier transforms -- and rapid descent test functions; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171290000655
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A classical Fock space consists of functions of the form, Φ ↔ ( ϕ 0, ϕ 1, …, ϕ q, … ), whereϕ 0 ∈ C andϕ q ∈ L 2 ( R 3 q ), q ≥ 1 . We will replace theϕ q, q ≥ 1 withq -symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.