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Hyponormal differential operators with discrete spectrum

Ismailov Z. I., Unluyol E.

Opuscula Mathematica

2010

Vol. 30, no. 1

79-94

In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.

Multipoint normal differential operators of first order

Ismailov Z. I.

Opuscula Mathematica

2009

Vol. 29, no. 4

399-414

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.