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

ISSN: 2148-1830
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

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,

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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).