Friedrich Haslinger
Convolution equations in spaces of entire functions
and related properties of conformal mappings
(18 pages)
Abstract.
In this paper we consider convolution equations in Frechet
and dual Frechet algebras of entire functions. The emphasis lies on
nonradial weight functions defining the algebras of entire functions.
With the help of various methods from functional analysis a necessary
conditon is derived for a convolution operator to be surjective.
Further we construct examples of nonsurjective
convolution operators. Then sufficient conditions for surjectivity
of convolution operators are discussed. For one complex variable,
certain properties of level sets of conformal mappings appear to be of some
importance in this context. On the other hand the examples of nonsurjective
convolution operators give some insight into the behavior
of related conformal mappings and yield new results in the
variational theory of conformal mappings.
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