×

Normal extensions of differential operators for degenerate first-order. (English) Zbl 07896214

MSC:

47Bxx Special classes of linear operators
47Axx General theory of linear operators
47Exx Ordinary differential operators
Full Text: DOI

References:

[1] Barbu, V.; Favini, A., Periodic problems for degenerate differential equations, Rend. Ist. Mat. Univ. Trieste, 28, 29-57, 1997 · Zbl 0916.34042
[2] E. A. Coddington, ‘‘Extension theory of formally normal and symmetric subspaces,’’ Mem. Am. Math. Soc. 134 (1973). · Zbl 0265.47023
[3] Biriuk, G.; Coddington, E. A., Normal extensions of unbounded formally normal operators, J. Math. Mech., 13, 617-638, 1964 · Zbl 0129.08603
[4] Goldstein, J. A., Semigroups of Linear Operators and Applications, 1985, New York: Oxford Univ. Press, New York · Zbl 0592.47034
[5] Gorbachuk, V. I.; Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations, 1991, Dordrecht: Kluwer Academic, Dordrecht · Zbl 0751.47025 · doi:10.1007/978-94-011-3714-0
[6] Krein, S. G., Linear Differential Equations in Banach Space, 1971, Providence, RI: Am. Math. Soc., Providence, RI
[7] Ismailov, Z. I., Formally-normal extensions of an operator, Differ. Uravn., 28, 905-907, 1992 · Zbl 0823.47043
[8] Ismailov, Z. I.; Karatash, H., Some necessary conditions for the normality of differential operator, Dokl. Math., 62, 277-279, 2000 · Zbl 1057.47512
[9] Ismailov, Z. I., On the normality of first-order differential operators, Bull. Pol. Acad. Sci. (Math.), 51, 139-145, 2003 · Zbl 1073.47048
[10] Ismailov, Z. I., Compact inverses of first-order normal differential operators, J. Math. Anal. Appl., 320, 266-278, 2006 · Zbl 1098.47041 · doi:10.1016/j.jmaa.2005.06.090
[11] Ismailov, Z. I.; Erol, M., Normal differential operators of first-order with smooth coefficients, Rocky MT J. Math., 42, 1100-1110, 2012 · Zbl 1244.47011 · doi:10.1216/RMJ-2012-42-2-633
[12] Maksudov, F. G.; Ismailov, Z. I., One necessary condition for normality of differential operators, Dokl. Math., 59, 422-424, 1999 · Zbl 0976.47026
[13] Sauer, N., Linear evolution equations in two Banach spaces, Proc. R. Soc. Edinburgh, 91, 287-303, 1982 · Zbl 0529.47028 · doi:10.1017/S0308210500017510
[14] Sauer, N.; Singleton, J. E., Evolution operators related to semi-groups of class (A), Semigroup Forum, 35, 317-335, 1987 · Zbl 0617.47030 · doi:10.1007/BF02573114
[15] Schmüdgen, K., Unbounded Self-Adjoint Operators on Hilbert Space, 2012, New York: Springer, New York · Zbl 1257.47001 · doi:10.1007/978-94-007-4753-1
[16] Sertbaş, M.; Yılmaz, F., Degenerate maximal hyponormal differential operators for the first order, Turkish J. Math., 43, 126-131, 2019 · Zbl 1486.47082 · doi:10.3906/mat-1805-13
[17] Showalter, R. E., Partial differential equations of Sobolev-Galperin type, Pacif. J. Math., 31, 787-793, 1963 · Zbl 0185.19002 · doi:10.2140/pjm.1969.31.787
[18] Stochel, J.; Szafraniec, F. H., On normal extensions of unbounded operators, I, Oper. Theory, 14, 31-55, 1985 · Zbl 0613.47022
[19] Stochel, J.; Szafraniec, F. H., On normal extensions of unbounded operators, II, Acta Sci. Math. (Szeged), 53, 153-177, 1989 · Zbl 0698.47003
[20] Stochel, J.; Szafraniec, F. H., “On normal part of an unbounded operator,” Nederl. Acad. Wetensch. Proc, Ser. A, 92, 495-503, 1989 · Zbl 0699.47020
[21] Sviridyuk, G. A.; Fedorov, V. E., Linear Sobolev Type Equations and Degenerate Semigroups of Operators, 2003, Utrecht: VSP, Utrecht · Zbl 1102.47061 · doi:10.1515/9783110915501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.