Characterizing compact families via the Laplace transform

The Laplace Transform for Locally Compact Abelian Groups.

Neutron Kinetics via Numerical Laplace Transform Inversion

A newly developed numerical Laplace transform inversion (NLTI) will be presented to determine the transient flux distribution within a subcritical fissile sample. The NLTI considered in this presentation has evolved to its present state over the past 10 years of application. The methodology adopted relies on the evaluation of the Bromwich contour through acceleration of the convergence of an in...

Compact Operators via the Berezin Transform

In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on ∂D. This result is new even when S equals a single Toeplitz operator. Our main result can be used to prove, via a unified approach, several previously known results about compact Toeplitz oper...

The Cayley Hamilton and Frobenius Theorems via the Laplace Transform

The Cayley Hamilton theorem on the characteristic polynomial of a matrix A and Frobenius’ theorem on minimal polynomial of A are deduced from the familiar Laplace transform formula L(eAt) = (sI − A)−1. This formula is extended to a formal power series ring over an algebraically closed field of characteristic 0, so that the argument applies in the more general setting of matrices over a field of...

Positive-part moments via the Fourier-Laplace transform

Abstract: Integral expressions for positive-part moments E Xp + (p > 0) of random variables X are presented, in terms of the Fourier-Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-par...