On real-analytic recurrence relations for cardinal exponential B-splines

  • Authors:

  • J. M. Aldaz;O. Kounchev;H. Render

  • Affiliations:

  • Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n., 26004 Logroòo, Spain;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria;Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n., 26004 Logroòo, Spain

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2007

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Abstract

Let L"N"+"1 be a linear differential operator of order N+1 with constant coefficients and real eigenvalues @l"1,...,@l"N"+"1, let E(@L"N"+"1) be the space of all C^~-solutions of L"N"+"1 on the real line. We show that for N=2 and n=2,...,N, there is a recurrence relation from suitable subspaces E"n to E"n"+"1 involving real-analytic functions, and with E"N"+"1=E(@L"N"+"1) if and only if contiguous eigenvalues are equally spaced.