Boundedly solvable degenerate differential operators for first order

Year 2018, Volume: 1 Issue: 1, 68 - 73, 11.03.2018

Pembe İpek , Zameddin İsmailov

https://doi.org/10.32323/ujma.387330

Cited By: 1

Abstract

Using the methods of operator theory all boundedly
solvable extensions of the minimal operator generated by degenerated
type differential-operators expression in the weighted Hilbert space
of vector-functions in finite interval in terms of boundary conditions.
Later on, the structure of spectrum of these type extensions will
be investigated.

Keywords

Degenerate differential-operator expression, Boundedly solvable operator, Spectrum

References

• [1] Favini, A. and Yagi, A., Degenerate differential equations in Banach Spaces, Marcel Dekker, Inc., New-York-Basel-Hong Kong, 1999.
• [2] Goldstein, J. A., Semigroups of linear operators and applications, Oxford University Press, New York and Oxford, 245 pp., 1985.
• [3] Hörmander L., On the theory of general partial differential operators, Acta. Math. 94, 162-166, 1955.
• [4] Vishik, M. I., On linear boundary problems for differential equations, Doklady Akad. Nauk SSSR (N.S) 65, 785-788, 1949.
• [5] Vishik, M. I., On general boundary problems for elliptic differential equations, Amer. Math. Soc. Transl. II 24, 107-172, 1963.