Displaying similar documents to “Operators and distributions”

Solution operators for convolution equations on the germs of analytic functions on compact convex sets in ℂ N

S. Melikhov, Siegfried Momm (1995)

Studia Mathematica

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G ⊂ ℂ N is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.

Surjective convolution operators on spaces of distributions.

Leonhard Frerick, Jochen Wengenroth (2003)

RACSAM

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We review recent developments in the theory of inductive limits and use them to give a new and rather easy proof for Hörmander?s characterization of surjective convolution operators on spaces of Schwartz distributions.

The cancellation law for inf-convolution of convex functions

Dariusz Zagrodny (1994)

Studia Mathematica

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Conditions under which the inf-convolution of f and g f □ g ( x ) : = i n f y + z = x ( f ( y ) + g ( z ) ) has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions f : X → ℝ ∪ + ∞ on a reflexive Banach space such that l i m ∥ x ∥ → ∞ f ( x ) / ∥ x ∥ = ∞ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.

Domains of integral operators

Iwo Labuda, Paweł Szeptycki (1994)

Studia Mathematica

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It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.