Functions in the Schwartz algebra that are invertible in the sense of Ehrenpreis

We consider the problem of obtaining the restrictions on the zero set of an entire function of exponential type under which this function belongs to the Schwartz algebra and invertible in the sense of Ehrenpreis.

The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series

The algebra of all Dirichlet series that are uniformly convergent in the half-plane of complex numbers with positive real part is investigated. When it is endowed with its natural locally convex topology, it is a non-nuclear Fréchet Schwartz space with basis. Moreover, it is a locally multiplicative algebra but not aQ-algebra. Composition operators on this space are also studied.

CHERN CHARACTER FOR THE SCHWARTZ ALGEBRA OF p-ADIC GL(n)

Let G denote the p-adic group GL(n), and let S(G) denote the Schwartz algebra of G. We construct a Chern character from the K-theory of the reduced C*-algebra of G to the periodic cyclic homology of S(G) which becomes an isomorphism after tensoring over ℤ with [Copf ].