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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, S โฅ ฮตI H for some ฮต > 0 in a Hilbert space H to an abstract buckling problem operator. In the concrete case where S = -ฮ| C โ 0 (ฮฉ) in L 2 (ฮฉ; d n x) for ฮฉ โ R n an open, bounded (and sufficiently regular) domain, this recovers, as a particular case of a general result due to G. Grubb, that the eigenvalue problem for the Krein Laplacian S K (i.e., the Krein-von Neumann extension of S),
๐ SIMILAR VOLUMES
We solve a boundary interpolation problem at a real point for generalized Nevanlinna functions, and use the result to prove uniqueness theorems for generalized Nevanlinna functions.
## Local energy decay for a class of hyperbolic equations with constant coefficients near infinity A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial variable coefficients. We shall deal with this equation in an N -dimensional exterior domain w
We study spectral properties of boundary integral operators which naturally arise in the study of the Maxwell system of equations in a Lipschitz domain ฮฉ โ R 3 . By employing Rellich-type identities we show that the spectrum of the magnetic dipole boundary integral operator (composed with an appropr