On convergence of Fourier series in discrete Jacobi-Sobolev spaces Articles uri icon

publication date

  • September 2023

start page

  • 703

end page

  • 720

issue

  • 9

volume

  • 34

International Standard Serial Number (ISSN)

  • 1065-2469

Electronic International Standard Serial Number (EISSN)

  • 1476-8291

abstract

  • In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach-Steinhaus theorem.

subjects

  • Mathematics

keywords

  • sobolev-type inner product; sobolev polynomials; jacobi polynomials; partial sum operator