On the normality of first-order differential operators

• Autorzy: Ismailov Z.
• Języki publikacji: EN

Abstrakty

EN

We investigate the relationship between the normality property of a first-order differential operator in a Hilbert space of vector-functions from the interval [O, 1] into a separable Hilbert space and the operator coefficients of the differential-operator expression which generates this operator.

Słowa kluczowe

EN

differential operator; self-adjoint operator; formally normal and normal operators; minimal and maximal operators

PL

operator różniczkowy; operator samosprzężony

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 2
• Strony: 139--145
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Ismailov Z.

• Black Sea Technical University, Faculty of Arts and Sciences, Department of Mathematics 61080, Trabzon, Turkey

Bibliografia

• [1] Yu. M. Berezanskiĭ, Expansions in eigenfunctions of self-adjoint operators, Amer. Math. Soc., 17 (1968).
• [2] G. Biriuk, E. A. Coddington, Normal extensions of unbounded formally normal operators, J. Math, and Mech., 13 (1964) 617-638.
• [3] B. N. Biyarov, M. O. Otelbayev, Description of normal extensions, Mat. Zametki, 53 (1993) 21-28.
• [4] E. A. Coddington, Normal extensions of formally normal operators, Pacif. J. Math., 10 (1960) 1203-1209.
• [5] E. A. Coddington, Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc., 134 (1973) 1-80.
• [6] R. H. Davis, Singular normal differential operators, Tech. Rep., Dep. Math., California Univ., 10 (1955).
• [7] V. I. Gorbachuk, M. L. Gorbachuk, Boundary value problems for differential-operator equations, Naukova Dumka, Kiev 1984.
• [8] Z. I. Ismailov, Formally normal extensions of an operator (in Belarusi), Differ. Uravn., 28 (1992) 905-907.
• [9] Z. I. Ismailov, Normal three-point boundary value problem for a differential-operator equation (in Russian), Sibirsk. Mat. Zh., 35 (1994) 1058-1061.
• [10] Y. Kilpi, Über lineare normale transformationen an Hilbertschen raum, Ann. Acad. Sci. Fenn. Math, AI, (159) (1993).
• [11] Y. Kilpi, Über das komplexe momenten problem, Ann. Acad. Sci. Fenn. Math., AI, (236) (1957).
• [12] Y. Kilpi, Über die anzahi der hypermaximalen normalen fort setzungen normaler transformationen, Ann. Univ. Turku. Ser., AI, (65) (1963).
• [13] L. A. Lusternik, V. J. Sobolev, The elements of functional analysis, Gordon and Breach, 1968.
• [14] F. G. Maksudov, Z. I. Ismailov, Normal extensions for differential operators of second order (in Belarusi), Differ. Uravn., 30 (1994) 1823-1824.
• [15] F. G. Maksudov, Z. I. Ismailov, Normal boundary value problems for differential equations of higher order, Turkish J. Math., 20 (1996) 141-151.
• [16] F. G. Maksudov, Z. I. Ismailov, Normal boundary value problems for differential equations of first order (in Russian), Dokl. Akad. Nauk, 350 (1996) 19-21.
• [17] Sz. Nagy, Spektraldarstellung linearen transformationen des Hilbertschen raumes, Ergeb. Math., (5) (1942) 33.
• [18] J. Stochel, F. H. Szafraniec, On normal extensions of unbounded operators, Oper. Theory, 14 (1985) 31-55.