Soon-Yeong Chung

Representation of quasianalytic ultradistributions

AbstractWe give the following representation theorem for a class containing quasianalytic ultradistributions and all the non-quasianalytic ultradistributions: Every ultradistribution in this class can be written as

Characterizations of ultradistributions with compact support and decomposition by support

u = P(\Delta )g(x) + h(x)

Fourier Hyperfunctions as the Boundary Values of Smooth Solutions of Heat Equations

whereg(x) is a bounded continuous function,h(x) is a bounded real analytic function andP(d/dt) is an ultradifferential operator. Also, we show that the boundary value of every heat function with some exponential growth condition determines an ultradistribution in this class. These results generalize the theorem of Matsuzawa [M] for the above class of quasianalytic ultradistributions and partially solve a question of A. Kaneko [Ka]. Our interest lies in the quasianalytic case, although the theorems do not exclude non-quasianalytic classes.

Distributions with exponential growth and Bochner-Schwartz theorem for Fourier hyperfunctions

We give an example of non trivial solution of the homogeneous Cauchy problem of the heat equation, which is, for each t, bounded in the space variables.

Structure of the extended Fourier hyperfunctions

In this paper we prove that every nonquasianalytic ultradistribution can be uniformly majorized by the behavior of test functions only on the support and that every ultradistribution with support in the union K1 U K2 of two compact sets can be decomposed as the sum of one with support in K1 and one with support in K2, along the context of Malgrange [ 17].