A general theorem on generation of moments-preserving cosine families by Laplace operators in C[0,1]

Abstract

We use Kelvin's method of images (Bobrowski in J. Evol. Equ. 10(3): 663-675, 2010; Semigroup Forum 81(3):435-445, 2010) to show that given two nonnegative integers i = j there exists a unique cosine family generated by a restriction of the Laplace operator in C [0,1], that preserves the moments of order i and j about 0, if and only if precisely one of these integers is zero.

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