JournalsprimsVol. 44, No. 4pp. 1097–1142

Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions

  • Paweł Domański

    Adam Mickiewicz University, Poznan, Poland
  • Michael Langenbruch

    Carl von Ossietzky Universität Oldenburg, Germany
Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions cover

Abstract

We develop the theory of hyperfunctions with values in a locally convex nonnecessarily metrizable space E and find necessary conditions and sufficient conditions such that a reasonable theory of E-valued hyperfunctions exists. In particular, we show that it exists for various spaces of distributions but there is no such theory for the spaces of real analytic functions and distributions with compact support. We also show that vector valued hyperfunctions can be interpreted as boundary values of vector valued harmonic or holomorphic functions and, in many cases, as suitable cohomology groups.

Cite this article

Paweł Domański, Michael Langenbruch, Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions. Publ. Res. Inst. Math. Sci. 44 (2008), no. 4, pp. 1097–1142

DOI 10.2977/PRIMS/1231263781