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On exact quadrature formulas for harmonic functions on polyhedra
Author(s):
Björn
Gustafsson;
Mihai
Putinar
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1427-1432.
MSC (2000):
Primary 65D32
Posted:
October 27, 1999
MathSciNet review:
1662233
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Abstract:
A classical quadrature result for analytic functions of a complex variable due to Motzkin and Schoenberg is extended to higher dimensions. A general scheme for integrating on polyhedra solutions of partial differential equations is discussed.
References:
- [1]
- Davis, Ph., Triangle formulas in the complex plane, Math. Comp. 18(1964), 569-577. MR 29:4874
- [2]
- Milanfar, P., Verghese, G.C., Karl, W.C., Wilsky, A.S., Reconstructing polygons from moments with connections to array processing, IEEE Trans. Signal Proc. 43(1995), 432- 443.
- [3]
- Golub, G.H., Milanfar, P., Varah, J., A stable numerical method for inversting shape from moments, preprint 1997.
- [4]
- Gustafsson, B., On mother bodies of convex polyhedra, SIAM J. Math. Anal. 29:5(1998). CMP 98:11
- [5]
- Henkin, G.M., Leiterer, J., Theory of functions on complex manifolds, Birkhäuser, Basel et al., 1984. MR 86i:32004
- [6]
- Hörmander, L., The analysis of linear partial differential operators .I, Springer-Verlag, Berlin et al., 1983. MR 85g:35002a
- [7]
- Siegel, D., Integration of harmonic functions over polygons, manuscript.
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Additional Information:
Björn
Gustafsson
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden
Email:
gbjorn@math.kth.se
Mihai
Putinar
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106
Email:
mputinar@math.ucsb.edu
DOI:
10.1090/S0002-9939-99-05295-8
PII:
S 0002-9939(99)05295-8
Received by editor(s):
July 2, 1998
Posted:
October 27, 1999
Additional Notes:
This research was partially supported by the National Science Foundation Grant DMS-9800666.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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