کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592671 1335125 2008 42 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Reduced Weyl asymptotics for pseudodifferential operators on bounded domains I. The finite group case
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Reduced Weyl asymptotics for pseudodifferential operators on bounded domains I. The finite group case
چکیده انگلیسی

Let G⊂O(n) be a compact group of isometries acting on n-dimensional Euclidean space Rn, and X a bounded domain in Rn which is transformed into itself under the action of G. Consider a symmetric, classical pseudodifferential operator A0 in L2(Rn) with G-invariant Weyl symbol, and assume that it is semi-bounded from below. We show that the spectrum of the Friedrichs extension A of the operator is discrete, and derive asymptotics for the number Nχ(λ) of eigenvalues of A less or equal λ and with eigenfunctions in the χ-isotypic component of L2(X) as λ→∞, giving also an estimate for the remainder term in case that G is a finite group. In particular, we show that the multiplicity of each unitary irreducible representation in L2(X) is asymptotically proportional to its dimension.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 255, Issue 4, 15 August 2008, Pages 777-818