On the Singular Value Decomposition of the Truncated Laplace Transform

The Laplace transform is a widely used integral operator. The spectral properties of the Laplace transform tend to complicate its numerical treatment; therefore, the closely related “truncated” Laplace transforms are often used in applications.

I will present efficient algorithms for the evaluation of the singular value decomposition of the truncated Laplace transform, and related numerical tools. I also will discuss the qualitative properties of the related functions and singular values, and illustrate the results via numerical experiments.