Some discontinuous translation-invariant linear forms

Translation-invariant linear operators

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, IR or R + which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous...

Non-Symmetric Translation Invariant Dirichlet Forms

In order to treat certain "non-symmetric" potential theories, It6 I-4] and Bliedtner [1] have generalized Beurling and Deny's theory of Dirichlet spaces by replacing the inner product in the Dirichlet space with a bilinear form defined on a real, regular functional space. This bilinear form, called a Dirichlet form, is supposed to be continuous and coercive, and furthermore to satisfy a "contra...

Nillsen Difference Spaces and Invariant Linear Forms

Translation-invariant Linear Forms and a Formula for the Dirac Measure

Following Schwartz [2 ] we denote by £>, 8 and S the complex vector spaces of all complex-valued infinitely differentiable functions on R where the functions of 2D have compact supports, the functions of 8 have arbitrary supports, and the functions of S (along with all their derivatives) are rapidly decreasing at infinity. We equip each of these spaces with its usual locally convex topology...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.