The General Form of Normal Quasi-Differential Operators for First Order and Their Spectrum

Year 2018, Volume: 8, 22 - 28, 30.06.2018

Pembe İpek , Bülent Yılmaz , Zameddin İsmailov

Abstract

In this work, the general form of all normal quasi-differential operators for rst order in the weighted Hilbert spaces of vector-functions on right semi-axis in term of boundary conditions has been found. Later on, spectrum set of these operators will be investigated.

Keywords

Formal normal and normal operator, quasi-differential operator, spectrum

References

• Coddington, E.A., Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc., 134(1973), 1–80.
• Davis, R.H., Singular Normal Differential Operators, Tech. Rep., Dep. Math., California Univ., 1955.
• Gorbachuk, V.I., Gorbachuk, M.L., On boundary value problems for a first-order differential equation with operator coefficients and the expansion in eigenvectors of this equation, Soviet Math. Dokl., 14(1)(1973), 244–248.
• Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94(1955), 161–248.
• Ismailov, Z.I., Compact inverses of first-order normal differential operators, J. Math., Anal. Appl. USA, 320(1)(2006), 266–278.
• Kilpi, Y., Über lineare normale transformationen in Hilbertschen raum, Ann. Acad. Sci. Fenn. Math. Ser. AI, 154(1953).
• Kilpi, Y., Über das komplexe momenten problem, Ann. Acad. Sci. Fenn. Math. Ser. AI, 236(1957), 1–32.
• Kilpi, Y., Über die anzahl der hypermaximalen normalen fort setzungen normalen transformationen, Ann. Univ. Turkuensis. Ser. AI, 65(1963).