On moments-preserving cosine families and semigroups in $C[0,1]$

Abstract

We use the newly developed Kelvin's method of images \cite{kosinusy,kelvin} to show existence of a unique cosine family generated by a restriction of the Laplace operator in $C[0,1]$, that preserves the first two moments. We characterize the domain of its generator by specifying its boundary conditions. Also, we show that it enjoys inherent symmetry properties, and in particular that it leaves the subspaces of odd and even functions invariant. Furthermore, we provide information on long-time behavior of the related semigroup.

arXiv comment20 pages, 2 figures

References in corpus (1)

• Well-posedness and spectral properties of heat and wave equations with non-local conditions

Cited by in corpus (4)

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• The heat equation under linear conditions on the moments in higher dimensions
• Diffusion processes on an interval under linear moment conditions
• Some remarks on the Krein--von Neumann extension of different Laplacians