Theory and use of functionals on the class of nonnegative polynomials and quadrature formulae

  • Authors:

  • A. V. Reztsov;G. C. Wake

  • Affiliations:

  • Division of Science & Technology, Tamaki Campus The University of Auckland Private Bag 92019, Auckland, New Zealand;Department of Mathematics, Tamaki Campus The University of Auckland, Auckland, New Zealand

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1997

Quantified Score

Hi-index 0.98

Visualization

Abstract

A functional of special type on classes of nonnegative polynomials is studied, which is helpful for the investigation of packings and cubature formulae. This functional in the classical case plays a very important role in analysis. The corresponding extremal problem is solved with the help of Legendre and Jacobi polynomials. Also, a new set of Gaussian quadrature formulae is obtained and used for two-dimensional integrals with circular symmetry.