Deficiency Indices of a Symmetric Ordinary Differential Operator with Infinitely Many Degeneration Points |
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Authors: | Yu. B. Orochko |
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Affiliation: | (1) Moscow State Institute of Electronics and Mathematics, Russia |
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Abstract: | Let H be the minimal symmetric operator in L2( ) generated by the differential expression (-1)n(c(x)f(n))(n), n 1, with a real coefficient c(x) that has countably many zeros without finite accumulation points and is infinitely smooth at all points x with c(x) 0. We study the value Def H of the deficiency indices of H. It is shown that DefH=+ if infinitely many zeros of c(x) have multiplicities p satisfying the inequality n – 1/2 < p < 2n – 1/2. Our second result pertains to the case in which the set of zeros of c(x) is bounded neither above nor below. Under this condition, Def H = 0 provided that the multiplicity of each zero is greater than or equal to 2n – 1/2. The multiplicities of zeros of c(x) are understood in the paper in a broader sense than in the standard definition. |
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Keywords: | symmetric operator deficiency indices degenerate ordinary differential operator |
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