Abstract
In this paper, we describe all maximal dissipative, maximal accretive and selfadjoint extensions of the minimal symmetric direct sum differential operators. Further using the equivalence of the Lax-Phillips scattering function and the Sz.-Nagy-Foiaş characteristic function we show that all eigen and associated functions of the maximal dissipative extension of the minimal symmetric direct sum operator are complete in $L_{w}^{2}(\Omega ),$ where $\Omega =\Omega _{1}\cup \Omega _{2},$ $\Omega _{1}=(0,c)$ and $\Omega _{2}=(c,\infty ).$
Citation
Bilender P. Allahverdiev . Ekin Ugurlu . "On selfadjoint dilation of the dissipative extension of a direct sum differential operator." Banach J. Math. Anal. 7 (2) 194 - 207, 2013. https://doi.org/10.15352/bjma/1363784231
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