کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425183 1633789 2016 45 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Semi-classical weights and equivariant spectral theory
ترجمه فارسی عنوان
وزن نیم کلاسیک و نظریه طیفی معادل آن
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

We prove inverse spectral results for differential operators on manifolds and orbifolds invariant under a torus action. These inverse spectral results involve the asymptotic equivariant spectrum, which is the spectrum itself together with “very large” weights of the torus action on eigenspaces. More precisely, we show that the asymptotic equivariant spectrum of the Laplace operator of any toric metric on a generic toric orbifold determines the equivariant biholomorphism class of the orbifold; we also show that the asymptotic equivariant spectrum of a Tn-invariant Schrödinger operator on Rn determines its potential in some suitably convex cases. In addition, we prove that the asymptotic equivariant spectrum of an S1-invariant metric on S2 determines the metric itself in many cases. Finally, we obtain an asymptotic equivariant inverse spectral result for weighted projective spaces. As a crucial ingredient in these inverse results, we derive a surprisingly simple formula for the asymptotic equivariant trace of a family of semi-classical differential operators invariant under a torus action.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 299, 20 August 2016, Pages 202-246
نویسندگان
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