M ‐functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
By B. M. Brown, Gerd Grubb, Ian Wood. 2008
88 citations recorded by the source corpus.
In this paper, we combine results on extensions of operators with recent results on the relation between the M ‐function and the spectrum, to examine the spectral behaviour of boundary value problems. M ‐functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the operator to possess spectral points that cannot be detected by the M ‐function (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9226d0e793a6bba98ac50d7d2d14a45a61add591
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples (2012, background): “…boundary triple for an elliptic operator from Section 1.2 can already be found in a slightly different context in [Grubb, 1968] and was studied in slight variations in [Brown, Grubb and Wood, 2009; Brown et al., 2009, 2008; Grubb; Malamud, 2010; Posili- cano, 2008; Posilicano and Raimondi, 2009].”
- A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, methodology): “[32] B. M. Brown, G. Grubb, and I. G. Wood, M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems, Math.”
- Boundary Value Problems, Weyl Functions, and Differential Operators (2020, methodology): “, [105, 169, 173, 359, 557, 643] and extends with some simple modifications to second-order and 2m-th order elliptic operators with variable coefficients.”