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Separation properties for Sturm-Liouville operators

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Abstract

Let q (x) be a positive function given on the interval I of the real axis; let P be the minimal operator generated in L2(0, +∞) by the differential expression P[·]=-d2/dx2+q(x); let Q be the operator of multiplication by the function q(x). If Dp* ⊂ Dq, then P [·] is said to be separated. In this note the separation of P[·] is proved for some growth regularity conditions on the fonction q (x), without assuming anything on its smoothness. One proves that if Dp* ⊂ DS, where S is the multiplication operator by the function s(x), satisfying some growth regularity condition, then DQ⊂ DS.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    K. Kh. Boimatov

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  1. K. Kh. Boimatov
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Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 349–359, September, 1973.

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Boimatov, K.K. Separation properties for Sturm-Liouville operators. Mathematical Notes of the Academy of Sciences of the USSR 14, 761–767 (1973). https://doi.org/10.1007/BF01147451

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  • DOI: https://doi.org/10.1007/BF01147451

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