Extensions of the matrix-valued$\ q-$Sturm-Liouville operators

Authors: BİLENDER PAŞAOĞLU, HÜSEYİN TUNA

Abstract: In this paper, we investigate the matrix-valued$\ q-$Sturm--Liouville problems. We establish an existence and uniqueness result. Later, we introduce the corresponding maximal and minimal operators for this system. Moreover, we give a criterion under which these operators are self-adjoint. Finally, we characterize extensions (maximal dissipative, maximal accumulative, and self-adjoint) of the minimal symmetric operator.

Keywords: Boundary value space, boundary condition, dissipative extensions, accretive extensions, self-adjoint extensions

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