International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1994 / Article

Open Access

Volume 17 |Article ID 356721 |

John Schmeelk, "Hankel transforms in generalized Fock spaces", International Journal of Mathematics and Mathematical Sciences, vol. 17, Article ID 356721, 14 pages, 1994.

Hankel transforms in generalized Fock spaces

Received21 Jul 1992
Revised06 Apr 1993


A classical Fock space consists of functions of the form,ϕ(ϕ0,ϕ1,,ϕq),where ϕ0 and ϕqLp(q), q1. We will replace the ϕq, q1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the inductive limit parameter, s, which sweeps out a scale of generalized Fock spaces.

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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