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

作者：Bobrowski Adam^*; Gregosiewicz Adam

来源：Semigroup Forum, 2014, 88(3): 689-701.

DOI：10.1007/s00233-013-9561-0

• Method of images
• Cosine families
• Strongly-continuous semigroup
• Differential operators with integral conditions

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 non-negative integers i not equal 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.

• 出版日期2014-6