Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642584 | Journal of Computational and Applied Mathematics | 2007 | 12 Pages |
Abstract
In an earlier publication a linear operator THar was defined as an unusual self-adjoint extension generated by each linear elliptic partial differential expression, satisfying suitable conditions on a bounded region Ω of some Euclidean space. In this present work the authors define an extensive class of THar-like self-adjoint operators on the Hilbert function space L2(Ω); but here for brevity we restrict the development to the classical Laplacian differential expression, with Ω now the planar unit disk. It is demonstrated that there exists a non-denumerable set of such THar-like operators (each a self-adjoint extension generated by the Laplacian), each of which has a domain in L2(Ω) that does not lie within the usual Sobolev Hilbert function space W2(Ω). These THar-like operators cannot be specified by conventional differential boundary conditions on the boundary of âΩ, and may have non-empty essential spectra.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
W.N. Everitt, L. Markus, M. Muzzulini, M. Plum,