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Frame measures for infinitely many measures


Abstract


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

DOI Code: 10.1285/i15900932v40n1p115

Keywords: Fourier frame; Plancherel theorem; spectral measure; frame measure; Bessel measure

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