A calculus approach to hyperfunctions III

Abstract

In the previous papers, [18] and [19], we have given some basis of a calculus approach to hyperfunctions. We have taken hyperfunctions with the compact support as initial values of the solutions of the heat equation. More precisely, let A′[K] be the space of analytic functionals supported by a compact subset K of Rn and let E(x, t) be the n-dimensional heat kernel given by.

Stability of an additive functional equation in the spaces of generalized functions

“…We also use the following famous result, socalled heat kernel method, which states as follows: Theorem 2.3 [23]. Let u ∈ S (Ê m ) .…”

Stability of Cubic Functional Equation in the Spaces of Generalized Functions

“…We refer to [17, Chapter VI] for pullbacks and to [16,18,20] for more details of (R n ) and Ᏺ (R n ).…”

Stability of Jensen equations in the space of generalized functions

“…As a matter of fact it is shown in [14] that the Gauss transform Gu(x, t) of u is a C ∞ solution of the heat equation and Gu(x, t) converges to u as t → 0 + in the following sense of generalized functions: for all test function ϕ,…”