Given general quasi-differential expressions , each of order n with complex coefficients and their formal adjoint are on the interval [ a , b ) respectively, we give a characterization of all regularly solvable operators and their adjoints generated by a general ordinary quasi-differential expression in the direct sum Hilbert spaces . The domains of these operators are described in terms of boundary conditions involving -solutions of the equations and their adjoint on the intervals [ a p , b p ) . This characterization is an extension of those obtained in the case of one interval with one and two singular end-points of the interval ( a , b ) , and is a generalization of those proved in the case of self-adjoint and J -self-adjoint differential operators as a special case, where J denotes complex conjugation.
KeywordsQuasi-Differential ExpressionsRegular and Singular EquationsMinimal and Maximal OperatorsRegularly Solvable Operators<i>J</i>-Self-Adjoint ExtensionBoundary Conditions
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