کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896690 | 1630596 | 2018 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Translational absolute continuity and Fourier frames on a sum of singular measures
ترجمه فارسی عنوان
تداوم مطلق انتقال و فریم فوریه بر روی مجموع اقدامات منحصر به فرد
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
A finite Borel measure μ in Rd is called a frame-spectral measure if it admits an exponential frame (or Fourier frame) for L2(μ). It has been conjectured that a frame-spectral measure must be translationally absolutely continuous, which is a criterion describing the local uniformity of a measure on its support. In this paper, we show that if any measures ν and λ without atoms whose supports form a packing pair, then νâλ+δtâν is translationally singular and it does not admit any Fourier frame. In particular, we show that the sum of one-fourth and one-sixteenth Cantor measure μ4+μ16 does not admit any Fourier frame. We also interpolate the mixed-type frame-spectral measures studied by Lev and the measure we studied. In doing so, we demonstrate a discontinuity behavior: For any anticlockwise rotation mapping Rθ with θâ ±Ï/2, the two-dimensional measure Ïθ(â
):=(μ4Ãδ0)(â
)+(δ0Ãμ16)(Rθâ1â
), supported on the union of x-axis and y=(cotâ¡Î¸)x, always admit a Fourier frame. Furthermore, we can find {e2Ïiãλ,xã}λâÎθ such that it forms a Fourier frame for Ïθ with frame bounds independent of θ. Nonetheless, ϱÏ/2 does not admit any Fourier frame.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 274, Issue 9, 1 May 2018, Pages 2477-2498
Journal: Journal of Functional Analysis - Volume 274, Issue 9, 1 May 2018, Pages 2477-2498
نویسندگان
Xiaoye Fu, Chun-Kit Lai,