Journal article
Spectral reciprocity and matrix representations of unbounded operators
Journal of functional analysis, Vol.261(3), pp.749-776
2011
DOI: 10.1016/j.jfa.2011.01.016
Abstract
We study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian. For an infinite discrete set X, we consider operators acting on Hilbert spaces of functions on X, and their representations as infinite matrices; the focus is on ℓ 2 ( X ) , and the energy space H E . In particular, we prove that these operators are always essentially self-adjoint on ℓ 2 ( X ) , but may fail to be essentially self-adjoint on H E . In the general case, we examine the von Neumann deficiency indices of these operators and explore their relevance in mathematical physics. Finally we study the spectra of the H E operators with the use of a new approximation scheme.
Details
- Title: Subtitle
- Spectral reciprocity and matrix representations of unbounded operators
- Creators
- Palle E.T Jorgensen - University of Iowa, Iowa City, IA 52246-1419, USAErin P.J Pearse - University of Oklahoma, Norman, OK 73019-0315 USA
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.261(3), pp.749-776
- DOI
- 10.1016/j.jfa.2011.01.016
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Grant note
- DMS-0457581 / NSF DMS-0602242 / University of Iowa Department of Mathematics NSF VIGRE
- Language
- English
- Date published
- 2011
- Academic Unit
- Mathematics
- Record Identifier
- 9983985924002771
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