-Topologies on the Test Function Algebra
On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...
On convergence in some subspaces of generalized functions
On distributions of rapid growth
On E. Borel's Theorem.
On functional equations of complex powers.
On functions with vanishing local derivative
On infinite derivatives of continuous functions
On Multidimensional Generalizations Of Regularly Varying Functions And Tauberian And Abelian Theorems
On regular and absolutely regular distributions in .
On regular -distributions
On regular temperature distribution
On representation of temperate distributions
On sequentially M-integrable distributions
On some classes of infinitely decomposable Sobolev-Schwartz test functions
On some spaces of distributions
On tempered convolution operators
In this paper we show that if is a convolution operator in , and , then the zeros of the Fourier transform of are of bounded order. Then we discuss relations between the topologies of the space of convolution operators on . Finally, we give sufficient conditions for convergence in the space of convolution operators in and in its dual.
On the Bézout equation in the ring of periodic distributions
A corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.
On the canonical extensions for distributions in the space
On the continuity of quotient multipliers