A Cohen type inequality for Gegenbauer-Sobolev expansions Articles uri icon

publication date

  • January 2013

start page

  • 135

end page

  • 148

issue

  • 1

volume

  • 43

international standard serial number (ISSN)

  • 0035-7596

electronic international standard serial number (EISSN)

  • 1945-3795

abstract

  • We introduce the Sobolev-type inner product< f, g > = integral(1)(-1) f(x) g(x) d mu(x) + M[f(1) g(1) + f(-1) g(-1)]+ N[f' (1)g' (1) + f' (-1)g' (-1)],whered mu(x) = Gamma(2 alpha + 2)/2(2 alpha) + (1)Gamma(2) (alpha + 1) (1 - x(2))(alpha) dx,M, N >= 0, alpha > - 1.In this paper we prove a Cohen type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product.

keywords

  • gegenbauer-sobolev polynomials; orthogonal expansions; cohen type inequality