کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898200 | 1631324 | 2018 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A universal formula for generalized cardinal B-splines
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A universal formula for generalized cardinal B-splines A universal formula for generalized cardinal B-splines](/preview/png/8898200.png)
چکیده انگلیسی
We introduce a universal and systematic way of defining a generalized B-spline based on a linear shift-invariant (LSI) operator L (a.k.a. Fourier multiplier). The generic form of the B-spline is βL=LdLâ1δ where Lâ1δ is the Green's function of L and where Ld is the discretized version of the operator that has the smallest-possible null space. The cornerstone of our approach is a main construction of Ld in the form of an infinite product that is motivated by Weierstrass' factorization of entire functions. We show that the resulting Fourier-domain expression is compatible with the construction of all known B-splines. In the special case where L is the derivative operator (linked with piecewise-constant splines), our formula is equivalent to Euler's celebrated decomposition of sinc(x)=sinâ¡(Ïx)Ïx into an infinite product of polynomials. Our main challenge is to prove convergence and to establish continuity results for the proposed infinite-product representation. The ultimate outcome is the demonstration that the generalized B-spline βL generates a Riesz basis of the space of cardinal L-splines, where L is an essentially arbitrary pseudo-differential operator.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 45, Issue 2, September 2018, Pages 341-358
Journal: Applied and Computational Harmonic Analysis - Volume 45, Issue 2, September 2018, Pages 341-358
نویسندگان
Arash Amini, Ramtin Madani, Michael Unser,