Solving a class of multivariate integration problems via Laplace techniques

Volume 28 / 2001

Jean B. Lasserre, Eduardo S. Zeron Applicationes Mathematicae 28 (2001), 391-405 MSC: 65D30, 65D15, 65R10. DOI: 10.4064/am28-4-2


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.


  • Jean B. LasserreLAAS-CNRS
    7 Avenue du Colonel Roche
    31077 Toulouse Cedex 4, France
  • Eduardo S. ZeronDepartamento de Matemáticas
    Apdo. Postal 14740
    México, D.F. 07000, Mexico

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