Description of Maximally Dissipative Quasi-Differential Operators for First Order

Yıl 2018, Cilt: 22 Sayı: 6, 1651 - 1658, 01.12.2018

Pembe Ipek Al

https://doi.org/10.16984/saufenbilder.407581

Cited By: 2

Öz

In this
work, the general form of maximally dissipative extensions of the minimal
operator generated by first order linear symmetric quasi-differential
expression in the weighted Hilbert space of vector-functions at right
semi-infinite interval has been found. Later on, geometry of spectrum of these
extensions is investigated.

Anahtar Kelimeler

deficiency indices, space of boundary values, dissipative operator

Kaynakça

• Referans1 V. I. Gorbachuk and M. I. Gorbachuk, “Boundary value problems for operator differential equations, ”Kluwer, Dordrecht, 1999.
• Referans2 J. Von Neumann, “Allgemeine eigenwerttheorie hermitescher funktionaloperatoren,” Math. Ann., vol. 102, pp. 49-131, 1929.
• Referans3 C. Fischbacher, “On the Theory of Dissipative Extensions,” PhD Thesis, University of Kent School of Mathematics, Statistic and Actuarial Science, Canterbury, 2017.
• Referans4 B. Sz.-Nagy and C. Foias, “Analyse harmonique des operateurs de L’ espace de Hilbert,” Masson, Paris and Akad Kiodo, Budapest, 1997 (English transl, North-Holland, Amesterdam and Akad Kiado, Budapest: 1970).
• Referans5 F. S. Rofe-Beketov and A. M. Kholkin, “Spectral analysis of differential operators.,” World Scientific Monograph Series in Mathematics, vol. 7, 2005.
• Referans6 L. Hörmander, “On the theory of general partial differential operators,” Acta Mathematica, vol. 94, pp. 161-248, 1955.