کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11010179 | 1812364 | 2019 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Limits of calculating the finite Hilbert transform from discrete samples
ترجمه فارسی عنوان
محدودیت محاسبه تبدیل هیلبرت محدود از نمونه های گسسته
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
This paper studies the problem of calculating the finite Hilbert transform fË=Hf of functions f from the set B of continuous functions with a continuous conjugate fË based on discrete samples of f. It is shown that all sampling based linear approximations which satisfy three natural axioms diverge strongly on B in the uniform norm. More precisely, we consider sequences {HN}NâN of linear approximation operators HN:BâB such that the calculation of HNf is based on discrete samples of f and which satisfies two additional natural axioms. We show that for all such sequences {HN}NâN there always exists an fâB such that limNâââ¡âHNfââ=+â. Moreover, it is shown that on the subset B1/2 of all fâB with finite Dirichlet energy an even larger class of sampling based approximation sequences diverges weakly, i.e. for all such sequences there always exists an fâB1/2 such that limsupNâââHNfââ=+â.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 46, Issue 1, January 2019, Pages 66-93
Journal: Applied and Computational Harmonic Analysis - Volume 46, Issue 1, January 2019, Pages 66-93
نویسندگان
Holger Boche, Volker Pohl,