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The Krein-von Neumann extension revisited. (English) Zbl 07513902

Summary: We revisit the Krein-von Neumann extension in the case where the underlying symmetric operator is strictly positive and apply this to derive the explicit form of the Krein-von Neumann extension for singular, general (i.e., three-coefficient) Sturm-Liouville operators on arbitrary intervals. In particular, the boundary conditions for the Krein-von Neumann extension of the strictly positive minimal Sturm-Liouville operator are explicitly expressed in terms of generalized boundary values adapted to the (possible) singularity structure of the coefficients near an interval endpoint.

MSC:

34B09 Boundary eigenvalue problems for ordinary differential equations
34B24 Sturm-Liouville theory
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34B20 Weyl theory and its generalizations for ordinary differential equations
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)

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