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.


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.)


Full Text: DOI


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