The Essential Spectrum of Neumann Laplacians on Some Bounded Singular Domains (1991)
by
Rainer Hempel
,
Luis A. Seco
,
Barry Simon
| Venue: | JOURNAL OF FUNCTIONAL ANALYSIS 102, 448483 (1991) |
| Citations: | 21 - 3 self |
BibTeX
@MISC{Hempel91theessential,
author = {Rainer Hempel and Luis A. Seco and Barry Simon},
title = { The Essential Spectrum of Neumann Laplacians on Some Bounded Singular Domains},
year = {1991}
}
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Abstract
In the present paper we consider Neumann Laplacians on singular domains of the type “rooms and passages” or “combs” and we show that, in typical situations, the essential spectrum can be determined from the geometric data. Moreover, given an arbitrary closed subset S of the non-negative reals, we construct domains Q = Q(S) such that the essential spectrum of the Neumann Laplacian on R is just this set S.
