American Institute of Mathematical Sciences

September  2015, 20(7): 1877-1895. doi: 10.3934/dcdsb.2015.20.1877

Functionals-preserving cosine families generated by Laplace operators in C[0,1]

 1 Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland, Poland, Poland

Received  May 2014 Revised  March 2015 Published  July 2015

Let $C[0,1]$ be the space of continuous functions on the unit interval $[0,1]$. A cosine family $\{C(t), t \in \mathbb{R}\}$ in $C[0,1]$ is said to be Laplace-operator generated, if its generator is a restriction of the Laplace operator $L\colon f \mapsto f''$ to a suitable subset of $C^2[0,1].$ The family is said to preserve a functional $F \in (C[0,1])^*$ if for all $f \in C[0,1]$ and $t \in \mathbb{R},$ $FC(t)f = Ff.$ We study a class of pairs of functionals such that for each member of this class there is a unique Laplace-operator generated cosine family that preserves both functionals in the pair.
Citation: Adam Bobrowski, Adam Gregosiewicz, Małgorzata Murat. Functionals-preserving cosine families generated by Laplace operators in C[0,1]. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1877-1895. doi: 10.3934/dcdsb.2015.20.1877
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