The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consider Laplace transforms of bounded functions. Our Tauberian theorem does not allow first-order poles on the imaginary axis, but any milder singularities, characterized by pseudofunction boundary behavior, are permissibl...

For stochastic C0-semigroups on L1-spaces there is a wealth of results that show strong convergence to an equilibrium as t ? ?, given the semigroup contains partial integral operator. This has plenty applications transport equations and in mathematical biology. However, up now operators do not play prominent role theorems which yield uniform rather than only convergence. In this article we prov...

In the classical parking problem, unit intervals (“car lengths”) are placed uniformly at random without overlapping. The process terminates saturation, i.e. until no more can be stowed. this paper, we present a generalization of problem in which with an exponential distribution rate parameter $$\lambda $$ . We show that mathematical expectation number saturation satisfies certain integral equat...