On multiple node Gaussian quadrature formulae
Author:
David L. Barrow
Journal:
Math. Comp. 32 (1978), 431-439
MSC:
Primary 41A55; Secondary 65D32
DOI:
https://doi.org/10.1090/S0025-5718-1978-0482257-0
MathSciNet review:
482257
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be odd positive integers and
. Let
be an extended Tchebycheff system on
. Let L be a positive linear functional on
. We prove that L has a unique representation in the form








- [1] Samuel Karlin and Allan Pinkus, Gaussian quadrature formulae with multiple nodes, Studies in spline functions and approximation theory, Academic Press, New York, 1976, pp. 113–141. MR 0477575
- [2] Samuel Karlin and William J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0204922
- [3] M. G. Kreĭn and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk (N. S.) 3 (1948), no. 1(23), 3–95 (Russian). MR 0027128
- [4] J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher; Notes on Mathematics and its Applications. MR 0433481
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1978-0482257-0
Article copyright:
© Copyright 1978
American Mathematical Society