کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4591193 1335015 2010 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Positive commutators at the bottom of the spectrum
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Positive commutators at the bottom of the spectrum
چکیده انگلیسی

Bony and Häfner have recently obtained positive commutator estimates on the Laplacian in the low-energy limit on asymptotically Euclidean spaces; these estimates can be used to prove local energy decay estimates if the metric is non-trapping. We simplify the proof of the estimates of Bony–Häfner and generalize them to the setting of scattering manifolds (i.e. manifolds with large conic ends), by applying a sharp Poincaré inequality. Our main result is the positive commutator estimateχI(H2Δg)i2[H2Δg,A]χI(H2Δg)⩾CχI(H2Δg)2, where H↑∞H↑∞ is a large parameter, I   is a compact interval in (0,∞)(0,∞), and χIχI its indicator function, and where A   is a differential operator supported outside a compact set and equal to (1/2)(rDr+(rDr)∗)(1/2)(rDr+(rDr)∗) near infinity. The Laplacian can also be modified by the addition of a positive potential of sufficiently rapid decay—the same estimate then holds for the resulting Schrödinger operator.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 259, Issue 2, 15 July 2010, Pages 503–523
نویسندگان
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