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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Integration and homogeneous functions


Author: Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 127 (1999), 813-818
MSC (1991): Primary 65D30
DOI: https://doi.org/10.1090/S0002-9939-99-04930-8
MathSciNet review: 1610733
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Abstract: We show that integrating a (positively) homogeneous function $f$ 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.


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Additional Information

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex 4, France
Email: lasserre@laas.fr

DOI: https://doi.org/10.1090/S0002-9939-99-04930-8
Keywords: Numerical integration in $R^n$, homogeneous functions
Received by editor(s): July 8, 1997
Communicated by: David H. Sharp
Article copyright: © Copyright 1999 American Mathematical Society