Studies on the Domains of Regularly Solvable Operators in the Direct Sum Spaces | Chapter 12 | Recent Advances in Mathematical Research and Computer Science Vol. 6

 We give a characterization of all regularly solvable operators and their adjoints generated by a general ordinary quasi-differential expressions (jp )in the direct sum Hilbert spaces L (w )2 (a p,b p),p=1,...,N, given a general quasi-differential expressions (1), (2),..., (n) each of order n with complex coefficients and their formal adjoint are 1+, On the intervals [a p, b p], the domains of these operators are characterised in terms of boundary conditions involving L (w)2 (a p,b p)-solutions of the equations _(jp) [y] = wy and its adjoint _jp+ [z] = wz (). This characterization is a generalisation of those proved in the case of self-adjoint and J-self-adjoint differential operators as special cases, where J denotes complex conjugation, and is an extension of those obtained in the case of one interval with one and two singular end-points of the interval (a, b).

Author(S) Details 

Sobhy El-Sayed Ibrahim
Department of Mathematics, Faculty of Science, Benha University, P.O. Box 13518 Benha, Egypt.

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