کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4619066 1339426 2010 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Non-spectral self-affine measure problem on the plane domain
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Non-spectral self-affine measure problem on the plane domain
چکیده انگلیسی

The self-affine measure μM,DμM,D corresponding to an expanding integer matrixM=[abcd]andD={(00),(10),(01)} is supported on the attractor (or invariant set) of the iterated function system {ϕd(x)=M−1(x+d)}d∈D{ϕd(x)=M−1(x+d)}d∈D. In the present paper we show that if (a+d)2=4(ad−bc)(a+d)2=4(ad−bc) and ad−bcad−bc is not a multiple of 3, then there exist at most 3 mutually orthogonal exponential functions in L2(μM,D)L2(μM,D), and the number 3 is the best. This extends several known results on the non-spectral self-affine measure problem. The proof of such result depends on the characterization of the zero set of the Fourier transform μˆM,D, and provides a way of dealing with the non-spectral problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 369, Issue 1, 1 September 2010, Pages 290–305
نویسندگان
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