Abstract
It is known that the Chebyshev polynomials of the first and second kinds are minimal in Lp on [−1,1] with respect to appropriate weight functions, namely certain powers of 1−x2, for 1≤p≤∞. These properties are here exploited in two applications. First, convergence and optimality properties are established for a "complete" Chebyshev polynomial expansion method for the determination of indefinite integrals. Second, conjectures are derived concerning the near-minimality of the Laguerre polynomials L ±1/2n (2β ×) for β≃1 with respect to appropriate exponentially weighted Lp norms on [0,∞).
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© 1988 Springer-Verlag
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Mason, J.C. (1988). The Lp minimality and near-minimality of orthogonal polynomial approximation and integration methods. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083368
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DOI: https://doi.org/10.1007/BFb0083368
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