Perturbation of Orthogonal Fourier Expansions

  1. Guadalupe, J.J. 1
  2. Pérez, M. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Journal:
Journal of Approximation Theory

ISSN: 0021-9045

Year of publication: 1998

Volume: 92

Issue: 2

Pages: 294-307

Type: Article

DOI: 10.1006/JATH.1997.3129 SCOPUS: 2-s2.0-0040682243 WoS: WOS:000072158600007 GOOGLE SCHOLAR lock_openOpen access editor

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Abstract

In this paper, a generalized Jacobi measure on [-1, 1] is perturbed by exponentials of functionsbof bounded mean oscillation. If we consider the Fourier series in orthogonal polynomials associated to each modification, then certain estimates (uniform inn∈N andbbelonging to some neighbourhood of the origin) are obtained. As a consequence, the partial sum operators depend analytically on the functional parameterb. The case of the Bessel series is also considered. © 1998 Academic Press.