Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Published electronically: October 27, 1999
MathSciNet review: 1662233
Full-text PDF Free Access

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] Philip J. Davis, Triangle formulas in the complex plane, Math. Comp. 18 (1964), 569–577. MR 0167602, 10.1090/S0025-5718-1964-0167602-8
  • [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] G. M. Henkin and J. Leiterer, Theory of functions on complex manifolds, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], vol. 60, Akademie-Verlag, Berlin, 1984. MR 795028
  • [6] Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035
  • [7] Siegel, D., Integration of harmonic functions over polygons, manuscript.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 65D32

Retrieve articles in all journals with MSC (2000): 65D32

Additional Information

Björn Gustafsson
Affiliation: Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden

Mihai Putinar
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106

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