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Maximal Hyponormal Operator Extensions of First-order with Smooth Coefficients

Year 2019, , 290 - 294, 15.04.2019
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.

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.

Birinci Mertebeden Düzgün Katsayılı Maksimal Hiponormal Operatör Genişlemeleri

Year 2019, , 290 - 294, 15.04.2019
https://doi.org/10.17714/gumusfenbil.418418

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.

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.
There are 18 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Meltem Sertbaş 0000-0001-9606-951X

Publication Date April 15, 2019
Submission Date April 25, 2018
Acceptance Date October 1, 2018
Published in Issue Year 2019

Cite

APA Sertbaş, M. (2019). Birinci Mertebeden Düzgün Katsayılı Maksimal Hiponormal Operatör Genişlemeleri. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9(2), 290-294. https://doi.org/10.17714/gumusfenbil.418418