ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 42, 43 Kuribayashi, Yukio, Tottori University, Japan On pseudofourier transforms In [1] we introduced a concept of pseudofourier transforms using nonstandard analysis. We will show the definition without precise conditions. Let f(x, y) be a complex valued function defined on R×R^{+}. We define the pseudofourier transform PF(f, k), k ∈ N, of the function f(x, y) by

PF(f, k)(x, y) = ∫_{−∞}^{∞} f(t, y) exp(−y|t|^{k}) exp(−ixt)dt.

Our main result is the following Theorem: PF(f, 1)(x, y) = F(f)(x, y) a. e. x ∈ R, where F denotes the Fourier transform in the sense of the theory of hyperfunctions. In the case of k = 2, some results will be shown. Reference[1] Y. Kuribayashi, The Fourier transforms using nonstandard analysis, Domestic Publication of RIMS Kyoto Univ., 957(1996), 132-144.