Frame measures for infinitely many measures

Abstract

For every frame spectral measure , there exists a discrete measure as a frame measure. If is not a frame spectral measure, then there is not any general statement about the existence of frame measures for . This motivated us to examine Bessel and frame measures. We construct infinitely many measures which admit frame measures , and we show that there exist infinitely many frame spectral measures such that besides having a discrete frame measure, they admit continuous frame measures too.