The Kronecker Limit Formulas

Abstract

Let f be a function on R. We shall say that f tends to 0 rapidly at infinity if for each positive integer m the function $$x \mapsto {\left| x \right|^m}f(x)$$is bounded. We define the Schwartz space S to be the set of functions on R which are infinitely differentiable and which tend to 0 rapidly at infinity, as well as their derivatives of all orders.