【20页精品】Continuous and Discrete Fourier Frames for Fractal Measures

Abstract: Motivated by the existence problem of Fourier frames on fractal measures, weintroduce Bessel and frame measures for a given finite measure on $\br^d$, asextensions of the notions of Bessel and frame spectra that correspond to basesof exponential functions. Not every finite compactly supported Borel measureadmits frame measures. We present a general way of constructing B..