• Bulletin of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.483-493
• /
• 1999

We extend the Paley-Wiener-Schwartz theorem to the space of ultradistributions with respect to ultradifferentiable singular support and obtain its real version. That is, we obtain the growth condition in some tubular neighborhood of n of the Fourier transform of ultradistributions of Roumieu (or Beurling) type with ultradifferentiable singular support contained in a ball centered at the origin, and its real version.

• Journal of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.455-466
• /
• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.