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Seminar on analytic theory of differential equations
November 2, 2016 15:30, Moscow, Steklov Mathematical Institute, Room 440 (8 Gubkina)
 


On the deficiency numbers of ordinary differential operators

K. A. Mirzoev
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MP4 674.6 Mb

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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 $L_2$. In particular, among the themes under consideration are:
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.

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