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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.

On the normality of first-order differential operators

Ismailov Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 2

139-145

We investigate the relationship between the normality property of a first-order differential operator in a Hilbert space of vector-functions from the interval [O, 1] into a separable Hilbert space and the operator coefficients of the differential-operator expression which generates this operator.