Opuscula Math. 30, no. 1 (2010), 79-94
Hyponormal differential operators with discrete spectrum
Abstract. 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.
Keywords: hyponormal operators, differential operators, minimal and maximal operators, extension of operators, compact operators, eigenvalues, asymptotes of eigenvalues.
Mathematics Subject Classification: 47A20.
- Received: 2009-07-07.
- Revised: 2009-09-23.
- Accepted: 2009-10-23.