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On exact quadrature formulas
for harmonic functions on polyhedra


Authors: Björn Gustafsson and Mihai Putinar
Journal: Proc. Amer. Math. Soc. 128 (2000), 1427-1432
MSC (2000): Primary 65D32
DOI: https://doi.org/10.1090/S0002-9939-99-05295-8
Published electronically: October 27, 1999
MathSciNet review: 1662233
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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: https://doi.org/10.1090/S0002-9939-99-05295-8
Received by editor(s): July 2, 1998
Published electronically: October 27, 1999
Additional Notes: This research was partially supported by the National Science Foundation Grant DMS-9800666.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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