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SEMINARS |
Seminar on analytic theory of differential equations
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On the deficiency numbers of ordinary differential operators K. A. Mirzoev |
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Abstract: In the talk we will discuss some problems connected to the deficiency index of a minimal operator generated by an ordinary symmetric differential expression on the semiaxis in the space 1) The definition of a quasi-differential expression (a differential expression with non-smooth coefficients), of a minimal operator generated by this expression, and of its deficiency numbers. 2) The divergent form of a real differential expression with smooth coefficients and McLeod's conjecture. 3) A criterium of the maximality of the deficiency numbers of a minimal operator in terms of the Cauchy function. 4) The limit point and the limit disc for the Sturm–Liouville operator. 5) Some open problems. |