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A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

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Mathematical Physics, Spectral Theory and Stochastic Analysis

Part of the book series: Operator Theory: Advances and Applications ((APDE,volume 232))

Abstract

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein–von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, ≥ ε ℋ for some ε > 0 in a Hilbert space 210B to an abstract bucklingpr oblem operator.

Mathematics Subject Classification (2010). Primary 35J25, 35J40, 35P15; secondary 35P05, 46E35, 47A10, 47F05.

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  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Mark S. Ashbaugh, Fritz Gesztesy & Marius Mitrea

  2. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, USA

    Roman Shterenberg

  3. Faculty of Mathematics, Nordbergstrasse 15, A-1090, Wien, Austria

    Gerald Teschl

  4. International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Wien, Austria

    Gerald Teschl

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Dedicated with great pleasure to Michael Demuth on the occasion of his 65th birthday

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Ashbaugh, M.S., Gesztesy, F., Mitrea, M., Shterenberg, R., Teschl, G. (2013). A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains. In: Demuth, M., Kirsch, W. (eds) Mathematical Physics, Spectral Theory and Stochastic Analysis. Operator Theory: Advances and Applications(), vol 232. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0591-9_1

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