Boundedly solvable degenerate differential operators for first order
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.
