کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774990 | 1413572 | 2017 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study a recent result of Bourgain, Clozel and Kahane, a version of which states that a sufficiently nice function f:RâR that coincides with its Fourier transform and vanishes at the origin has a root in the interval (c,â), where the optimal c satisfies 0.41â¤câ¤0.64. A similar result holds in higher dimensions. We improve the one-dimensional result to 0.45â¤câ¤0.594, and the lower bound in higher dimensions. We also prove that extremizers exist, and have infinitely many double roots. With this purpose in mind, we establish a new structure statement about Hermite polynomials which relates their pointwise evaluation to linear flows on the torus, and applies to other families of orthogonal polynomials as well.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 451, Issue 2, 15 July 2017, Pages 678-711
Journal: Journal of Mathematical Analysis and Applications - Volume 451, Issue 2, 15 July 2017, Pages 678-711
نویسندگان
Felipe Gonçalves, Diogo Oliveira e Silva, Stefan Steinerberger,