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

✍ Scribed by A.V. Reztsov; G.C. Wake

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 702 KB
• Volume: 25
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(97)00038-1

✦ Synopsis

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 csse 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.