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

Let LN+1 be a linear differential operator of order N + 1 with constant coefficients and real eigenvalues 1, . . . , N+1, let E( N+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N 2 and n = 2, . . . , N, there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, and with EN+1 =E( N+1) if and only if contiguous eigenvalues are equally spaced. © 2006 Elsevier Inc. All rights reserved. MSC: primary 41A15; secondary 35J40; 31B30

• Type: Journal
• Year: 2007
• Where: JAT
• Authors: J. M. Aldaz, Ognyan Kounchev, Hermann Render
• Keywords: Constant Coefficients, JAT 2007, Real Eigenvalues, Real Line