کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9495875 1335196 2005 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectral properties of Jacobi matrices and sum rules of special form
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Spectral properties of Jacobi matrices and sum rules of special form
چکیده انگلیسی
In this article, we relate the properties of elements of a Jacobi matrix from certain class to the properties of its spectral measure. The main tools we use are the so-called sum rules introduced by Case in [Orthogonal polynomials from the viewpoint of scattering theory, J. Math. Phys. 15 (1974) 2166-2174; Orthogonal polynomials, II. J. Math. Phys. 16 (1975) 1435-1440]. Later, the sum rules were efficiently applied by Killip-Simon [Sum rules for Jacobi matrices and their applications to spectral theory. Ann. Math. 158 (2003) 253-321] to the spectral analysis of Jacobi matrices. We use a modification of the method that permits us to work with sum rules of higher orders. As a corollary of the main theorem, we obtain a counterpart of a result of Molchanov-Novitskii-Vainberg [First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator, Comm. Math. Phys. 216 (2001) 195-213] for a “continuous” Schrödinger operator on a half-line.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 227, Issue 1, 1 October 2005, Pages 1-29
نویسندگان
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