共查询到20条相似文献,搜索用时 46 毫秒
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Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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Paolo Boggiatto Carmen Fernández Antonio Galbis 《Applied and Computational Harmonic Analysis》2017,42(1):65-87
Inspired by results of Kim and Ron, given a Gabor frame in , we determine a non-countable generalized frame for the non-separable space of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences. 相似文献
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A finite Borel measure μ in is called a frame-spectral measure if it admits an exponential frame (or Fourier frame) for . 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 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 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 with , the two-dimensional measure , supported on the union of x-axis and , always admit a Fourier frame. Furthermore, we can find such that it forms a Fourier frame for with frame bounds independent of θ. Nonetheless, does not admit any Fourier frame. 相似文献
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