Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

Integration and homogeneous functions

Author(s): Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 127 (1999), 813-818.
MSC (1991): Primary 65D30
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We show that integrating a (positively) homogeneous function on a compact domain $\Omega\subset R^n$ reduces to integrating a related function on the boundary $\partial{\Omega}$ . The formula simplifies when the boundary $\partial{\Omega}$ is determined by homogeneous functions. Similar results are also presented for integration of exponentials and logarithms of homogeneous functions.

References:

1.: A. Barvinok, Computing the volume, counting integral points, and exponential sums, Discrete & Computational Geometry 10 (1993), pp. 123-141. MR 94d:52005
2.: M. Brion, Points entiers dans les polyedres convexes, Ann. Sci. Ec. Norm. Sup., Serie IV, 21 (1988), pp. 653-663. MR 90d:52020
3.: J.B. Lasserre, An analytical expression and an algorithm for the volume of a convex polyhedron in , J. Optim. Theor. Appl. 39 (1983), pp. 363-377. MR 84m:52018
4.: J.B. Lasserre, Integration on a convex polytope, Proc. Amer. Math. Soc. 126 (1998), 2433-2441. CMP 97:15
5.: G. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press, 1986. MR 88a:00006
6.: M.E. Taylor, Partial Differential Equations: Basic Theory, Springer, New York, 1996. MR 98b:35002b


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS