کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5772467 1413371 2017 47 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Resonances for the Laplacian on products of two rank one Riemannian symmetric spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Resonances for the Laplacian on products of two rank one Riemannian symmetric spaces
چکیده انگلیسی
Let X=X1×X2 be a direct product of two rank-one Riemannian symmetric spaces of the noncompact type. We show that when at least one of the two spaces is isomorphic to a real hyperbolic space of odd dimension, the resolvent of the Laplacian of X can be lifted to a holomorphic function on a Riemann surface which is a branched covering of C. In all other cases, the resolvent of the Laplacian of X admits a singular meromorphic lift. The poles of this function are called the resonances of the Laplacian. We determine all resonances and show that the corresponding residue operators are given by convolution with spherical functions parameterized by the resonances. The ranges of these operators are finite dimensional and explicitly realized as direct sums of finite-dimensional irreducible spherical representations of the group of the isometries of X.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 4, 15 February 2017, Pages 1477-1523
نویسندگان
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