Maximal Hyponormal Operator Extensions of First-order with Smooth Coefficients

Year 2019, Volume: 9 Issue: 2, 290 - 294, 15.04.2019

Meltem Sertbaş

https://doi.org/10.17714/gumusfenbil.418418

Abstract

In this study, it is given all maximal
hyponormal extensions of first-order with smooth operator coefficients in
Hilbert valued function space on a finite interval. These extention is by means
of boundary values.Also, the structure of the spectrum of the maximal
hyponormal extensions is investigated.

Keywords

Differential operator, Extension, Hyponormal operator, Minimal and maximal operators, Spectrum

Birinci Mertebeden Düzgün Katsayılı Maksimal Hiponormal Operatör Genişlemeleri

Abstract

Bu
çalışmada sonlu bir aralıkta tanımlı Hilbert uzay değerli fonksiyonlar uzayında
tanımlı düzgün operatör katsayılı birinci mertebeden tüm maksimal hiponormal genişlemeleri
verilmiştir. Bu genişlemeler sınır değerleri anlamındadır. Ayrıca maksimal
hiponormal operatörlerin spektrum yapısı verilmiştir.

Keywords

Diferensiyel operatör, Genişleme, Hiponormal operatör, Minimal ve maksimal operatörler, Spektrum

References

• Berezansky, Y.M., 1968. Expansions in Eigenfunctions of Self-adjoint operators. Providence, RI: Amer. Math. Soc..
• Daleckii, J.U. and Krein, M.G., 1974. Stability of Solutions of Differential Equations in Banach Space. Providence, RI: Amer. Math. Soc..
• Dunford, N. ve Schwartz, J.T., 1963. Linear Operators , vol. II. New York, Interscience.
• Gorbachuk,V.I. ve Gorbachuk, M.L., 1991. Boundary Value Problems for Operator Differential Equations. Dordrecht, Kluwer Academic.
• Giaquinta, M. ve Hildebrand, S., 2004. Calculus of Variations I. Springer-Verlang Berlin, Heidelberg, Germany.
• Ismailov, Z.I., 1998. Discreteness of the Spectrum of the First Order Normal Differential Operators. Doklady Mathematics, Birmingham, USA, 57, 32-33.
• Ismailov, Z.I., 2003. On the Normality of first-order differential operators. Bull. Pol. Acad. Sci, 51, 139-145.
• Ismailov, Z.I., 2006. Compact Inverses of First-order Normal Differential Operators. J. Math. Anal. Appl., 320: 266-278.
• Ismailov, Z. ve Unluyol, E., 2010. Hyponormal Differential Operators with Discrete Spectrum. Opuscula Math., 30, 79-94.
• Ismailov, Z. ve Erol, M., 2012. Normal Differential Operators of First-order with Smooth Coefficients. Rocky Mt. J. Math., 42, 633-642.
• Janas, J., 1989. On Unbounded Hyponormal Operators, Ark. Mat., 27, 273-281.
• Jin, K.H., 1993. On unbounded Subnormal Operators. Bull. Korean Math. Soc., 30, 65-70.
• Krein, S.G., 1971. Linear Differential Equations in Banach Space, Providence, RI: Amer. Math. Soc..
• Ota, S. ve Schmüdgen, K., 1989. On Some Classes of Unbounded Operators, Integr. Equat. Oper. Th, 12, 211-226.
• Putnam, C.R., 1972. The Spectra of Unbounded Hyponormal Operators. Proc. Amer. Math. Soc.,31, 458- 464.
• Smüdgen, K., 2012. Unbounded Self-adjoint Operators on Hilbert Space. Springer Dordrecht Heidelberg, New York London.
• Stochel, J. ve Szafraniec, F.H., 1989. The Normal Part of an Unbounded Operator, Nederl. Akad. Wetensch. Proc. Ser. A , 92, 495-503.
• Von Neumann, J., 1929. Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren. Math. Ann., 102, 49-131.