ITERATIVE APPROXIMATIONS OF EXPONENTIAL BASES ON FRACTAL MEASURES
Abbreviated Journal Title
Numer. Funct. Anal. Optim.
Bessel sequence; Beurling dimension; Fractal; Frame; Iterated function; system; Riesz basic sequence; FUNCTION SYSTEMS; FRAMES; Mathematics, Applied
For some fractal measures it is a very difficult problem in general to prove the existence of spectrum (respectively, frame, Riesz and Bessel spectrum). In fact there are examples of extremely sparse sets that are not even Bessel spectra. In this article, we investigate this problem for general fractal measures induced by iterated function systems (IFS). We prove some existence results of spectra associated with Hadamard pairs. We also obtain some characterizations of Bessel spectrum in terms of finite matrices for affine IFS measures, and one sufficient condition of frame spectrum in the case that the affine IFS has no overlap.
Numerical Functional Analysis and Optimization
"ITERATIVE APPROXIMATIONS OF EXPONENTIAL BASES ON FRACTAL MEASURES" (2012). Faculty Bibliography 2010s. 2511.