This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are stu...

This paper studies the relationship between the singular trace of a weak trace class operator and the asymptotic behaviour of its ζ-function at its leading singularity. For Dixmier measurable and universally measurable operators we describe their measurability in terms of the behaviour of the ζ-function. We use recent advances in singular trace theory and a new approach based on Tauberian theor...

The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a packet results in the loss of the entire message. Messages arrive to the M/GI/1 finite buffer model and can be lost in two cases as either at least one of it...

This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic expansion for the Taylor coefficients ofthe function. This approach is based on contour integration using Cauchy’s formula and Hankel-like contours. It constitutes an alternative to either Darboux’s method ...