Journal article
Harmonic analysis on tori
Acta applicandae mathematicae, Vol.10(1), pp.87-99
09/1987
DOI: 10.1007/BF00046583
Abstract
We consider measurable subsets Ω∋{ofR}n with 0<m(Ω)<∞, and we assume that Ω has a spectral set Λ. (In the special case when Ω is also assumed open, Λ may be obtained as the joint spectrum of a family of commuting self-adjoint operators {H k: 1≤k≤n} in L 2 (Ω) such that each H k is an extension of i(∂/∂x k) on C c ∞(Ω), k=1, ..., n.)
It is known that Ω is a fundamental domain for a lattice if Λ is itself a lattice. In this paper, we consider a class of examples where Λ is not assumed to be a lattice. Instead Λ is assumed to have a certain inhomogeneous form, and we prove a necessary and sufficient condition for Ω to be a fundamental domain for some lattice in {ofR}n. We are thus able to decide the question, ‘fundamental domain or not’, by considering only properties of the spectrum Λ. Our criterion is obtained as a corollary to a theorem concerning partitions of sets Ω which have a spectrum of inhomogeneous form.
Details
- Title: Subtitle
- Harmonic analysis on tori
- Creators
- Palle E T JørgensenSteen Pedersen
- Resource Type
- Journal article
- Publication Details
- Acta applicandae mathematicae, Vol.10(1), pp.87-99
- DOI
- 10.1007/BF00046583
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- Language
- English
- Date published
- 09/1987
- Academic Unit
- Mathematics
- Record Identifier
- 9983986088102771
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