کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774607 | 1413563 | 2017 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Vanishing Fourier coefficients and the expression of functions in L2(T) as sums of generalised differences
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
If gâL2([0,2Ï]) let gË be the sequence of Fourier coefficients of g, let D denote differentiation and let I denote the identity operator. Given α,βâZ, we consider the operator D2âi(α+β)DâαβI on the second order Sobolev space of L2([0,2Ï]). The multiplier of this operator is â(nâα)(nâβ) considered as a function of nâZ, so that gË(α)=gË(β)=0 for any function g in the range of the operator. Let δx denote the Dirac measure at x, and let â denote convolution. If bâ[0,2Ï] let λb be the measure2â1[(eib(αâβ2)+eâib(αâβ2)]δ0â2â1[(eib(α+β2)δb+eâib(α+β2)δâb]. A function of the form λbâf is called a generalised difference, and we let F be the family of functions h such that h is a sum of five generalised differences. It is shown that for gâL2([0,2Ï]), gâF if and only if gË(α)=gË(β)=0. Consequently, F is a Hilbert subspace of L2([0,2Ï]) and it is the range of D2âi(α+β)DâαβI. The methods use partitions of intervals and estimates of integrals in Euclidean space. There are applications to the automatic continuity of linear forms in abstract harmonic analysis.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 455, Issue 2, 15 November 2017, Pages 1425-1443
Journal: Journal of Mathematical Analysis and Applications - Volume 455, Issue 2, 15 November 2017, Pages 1425-1443
نویسندگان
Rodney Nillsen,