کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9495777 | 1335185 | 2005 | 58 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let (M,g) be a globally symmetric space of noncompact type, of arbitrary rank, and Î its Laplacian. We introduce a new method to analyze Î and the resolvent (Î-Ï)-1; this has origins in quantum N-body scattering, but is independent of the 'classical' theory of spherical functions, and is analytically much more robust. We expect that, suitably modified, it will generalize to locally symmetric spaces of arbitrary rank. As an illustration of this method, we prove the existence of a meromorphic continuation of the resolvent across the continuous spectrum to a Riemann surface multiply covering the plane. We also show how this continuation may be deduced using the theory of spherical functions. In summary, this paper establishes a long-suspected connection between the analysis on symmetric spaces and N-body scattering.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 228, Issue 2, 15 November 2005, Pages 311-368
Journal: Journal of Functional Analysis - Volume 228, Issue 2, 15 November 2005, Pages 311-368
نویسندگان
Rafe Mazzeo, András Vasy,