On convergence of Fourier series in discrete Jacobi-Sobolev spaces. (English) Zbl 1519.42007
Authors’ 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 shown that this Sobolev space is the first category which implies that it is not possible to apply the Banach-Steinhaus theorem.
Reviewer: Sorin Gheorghe Gal (Oradea)
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 33C47 | Other special orthogonal polynomials and functions |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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