Abstract
Norm estimates from above and below for partial sum operators of ultraspherical and Laguerre expansions on a class of weighted Lebesgue spaces are established, using ultraspherical and Laguerre weights with parameters different from the parameters of the orthogonal expansions. It turns out that a suitable shifting of the parameters leads to a considerable reduction of the rate of growth of the operator norms. In this way projection operators on weighted Lebesgue spaces can be constructed, the norms of which are smaller than those of the corresponding partial sums. Thus first upper estimates for the minimal projections in these spaces are obtained.
This author was supported by a DFG grant (Ne 171/4) which is gratefully acknowledged.
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© 1981 Birkhäuser Verlag Basel
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Görlich, E., Markett, C. (1981). Projections with Norms Smaller than those of the Ultraspherical and Laguerre Partial Sums. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_19
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DOI: https://doi.org/10.1007/978-3-0348-9369-5_19
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