Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A note on Tchakaloff’s Theorem
HTML articles powered by AMS MathViewer

by Mihai Putinar
Proc. Amer. Math. Soc. 125 (1997), 2409-2414
DOI: https://doi.org/10.1090/S0002-9939-97-03862-8

Abstract:

A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.
References
  • H. Berens, H. J. Schmid, and Y. Xu, Multivariate Gaussian cubature formulae, Arch. Math. (Basel) 64 (1995), no. 1, 26–32. MR 1305657, DOI 10.1007/BF01193547
  • Curto, R.E. and Fialkow, L., Flat extensions of positive moment matrices: relations in analytic or conjugate terms, preprint 1994.
  • Mysovskikh, I.P., On Chakalov’s theorem, U.S.S.R. Comput. Math. and Math. Phys. 15(1975), no. 6, 221-227; (translation in Zh. Vychisl. Mat. i Mat. Fiz. 15(1975), no. 6, 1589-1593, 1627).
  • Mysovskikh, I.P., Interpolation cubature formulas (in Russian), Nauka, Moscow, 1981.
  • Bruce Reznick, Sums of even powers of real linear forms, Mem. Amer. Math. Soc. 96 (1992), no. 463, viii+155. MR 1096187, DOI 10.1090/memo/0463
  • A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0327006
  • Hans Joachim Schmid, Interpolatorische Kubaturformeln, Dissertationes Math. (Rozprawy Mat.) 220 (1983), 122 (German). MR 735919
  • Hans Joachim Schmid, Two-dimensional minimal cubature formulas and matrix equations, SIAM J. Matrix Anal. Appl. 16 (1995), no. 3, 898–921. MR 1337652, DOI 10.1137/S0895479893252404
  • Vladimir Tchakaloff, Formules de cubatures mécaniques à coefficients non négatifs, Bull. Sci. Math. (2) 81 (1957), 123–134 (French). MR 94632
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 65D32, 44A60
  • Retrieve articles in all journals with MSC (1991): 65D32, 44A60
Bibliographic Information
  • Mihai Putinar
  • Affiliation: Department of Mathematics, University of California, Riverside, California 92521
  • MR Author ID: 142835
  • Email: mputinar@math.ucr.edu
  • Received by editor(s): January 16, 1996
  • Received by editor(s) in revised form: February 22, 1996
  • Additional Notes: This work was partially supported by the National Foundation Grant DMS 9500954
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2409-2414
  • MSC (1991): Primary 65D32, 44A60
  • DOI: https://doi.org/10.1090/S0002-9939-97-03862-8
  • MathSciNet review: 1389533