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Matrix transformations of series of orthogonal polynomials

Borwein, David and Borwein, Peter and Jakimovski, Amnon (1995) Matrix transformations of series of orthogonal polynomials. [Preprint]

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      Abstract

      For a sequence of polynomials $(P_n)$ orthonormal on the interval $[-1,1]$, we consider the sequence of transforms $(g_ n)$ of the series $\sum_{k=0}^{\infty}a_kP_k(u)$ given by $g_n(u):=\text{$\sum_{k=0}^{\infty}b_{nk}a_kP_k(u)$}$. We establish necessary and sufficient conditions on the matrix $(b_{nk})$ for the sequence $(g_n)$ to converge uniformly on compact subsets of the interior of an appropriate ellipse to a function holomorphic on that interior.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: orthogonal polynomials, Jacobi, Chebyshev, matrix transforms, Norlund
      Subjects: 47-xx Operator theory > 47Bxx Special classes of linear operators
      30-xx Functions of a complex variable > 30Cxx Geometric function theory
      40-xx Sequences, series, summability > 40Gxx Special methods of summability
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/106

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