Solving a class of multivariate integration problems via Laplace techniques
Volume 28 / 2001
Applicationes Mathematicae 28 (2001), 391-405
MSC: 65D30, 65D15, 65R10.
DOI: 10.4064/am28-4-2
Abstract
We consider the problem of calculating a closed form expression for the integral of a real-valued function $f:{\Bbb R}^n\rightarrow {\Bbb R}$ on a set $S$. We specialize to the particular cases when $S$ is a convex polyhedron or an ellipsoid, and the function $f$ is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled numerically. Finally, a methodology is proposed for multivariate functions $f$ which have a (multidimensional) Laplace transform.
