کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607814 1337885 2010 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Smoothness of a function and the growth of its Fourier transform or its Fourier coefficients
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Smoothness of a function and the growth of its Fourier transform or its Fourier coefficients
چکیده انگلیسی
In a recent paper Bray and Pinsky [1] estimated the growth of f̂(ξ), the Fourier transform of f(x) where x∈Rd, by some moduli of smoothness. We show here that noticeably better results can be derived as an immediate corollary of previous theorems in [2]. The improvements include dealing with higher levels of smoothness and using the fact that for higher dimensions (when d≥2) the description of smoothness requires less information. Using a similar technique, we also deduce relations between the smoothness of f(x) for x∈Sd−1 or x∈Td and the growth of the coefficients of the expansion by spherical harmonic polynomials or trigonometric polynomials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 162, Issue 5, May 2010, Pages 980-986
نویسندگان
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