کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589889 1334917 2015 40 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Unitary groups and spectral sets
ترجمه فارسی عنوان
گروه های واحد و مجموعه های طیفی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
We study spectral theory for bounded Borel subsets of R and in particular finite unions of intervals. For Hilbert space, we take L2 of the union of the intervals. This yields a boundary value problem arising from the minimal operator D=12πiddx with domain consisting of C∞ functions vanishing at the endpoints. We offer a detailed interplay between geometric configurations of unions of intervals and a spectral theory for the corresponding self-adjoint extensions of D and for the associated unitary groups of local translations. While motivated by scattering theory and quantum graphs, our present focus is on the Fuglede-spectral pair problem. Stated more generally, this problem asks for a determination of those bounded Borel sets Ω in Rk such that L2(Ω) has an orthogonal basis of Fourier frequencies (spectrum), i.e., a total set of orthogonal complex exponentials restricted to Ω. In the general case, we characterize Borel sets Ω having this spectral property in terms of a unitary representation of (R,+) acting by local translations. The case of k=1 is of special interest, hence the interval-configurations. We give a characterization of those geometric interval-configurations which allow Fourier spectra directly in terms of the self-adjoint extensions of the minimal operator D. This allows for a direct and explicit interplay between geometry and spectra.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 268, Issue 8, 15 April 2015, Pages 2102-2141
نویسندگان
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