Opuscula Math. 29, no. 4 (2009), 399-414
Multipoint normal differential operators of first order
Abstract. In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.
Keywords: differential operator, formally normal and normal operator, multipoint minimal and maximal operators, extension, selfadjoint, accretive and unitary operators, class of compact operators, spectrum of an operators and its discreteness, asymptotics of eigenvalues, direct sum of spaces and operators.
Mathematics Subject Classification: 47A20.