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- W3016471569 abstract "Considering a finite Borel measure $ mu $ on $ mathbb{R}^d $, a pair of conjugate exponents $ p, q $, and a compatible semi-inner product on $ L^p(mu) $, we have introduced $ (p,q) $-Bessel and $ (p,q) $-frame measures as a generalization of the concepts of Bessel and frame measures. In addition, we have defined the notions of $ q $-Bessel sequence and $ q$-frame in the semi-inner product space $ L^p(mu) $. Every finite Borel measure $nu$ is a $(p,q)$-Bessel measure for a finite measure $ mu $. We have constructed a large number of examples of finite measures $ mu $ which admit infinite $ (p,q) $-Bessel measures $ nu $. We have showed that if $ nu $ is a $ (p,q) $-Bessel/frame measure for $ mu $, then $ nu $ is $ sigma $-finite and it is not unique. In fact, by using the convolutions of probability measures, one can obtain other $ (p,q) $-Bessel/frame measures for $ mu $. We have presented a general way of constructing a $ (p,q) $-Bessel/frame measure for a given measure." @default.
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- W3016471569 date "2020-04-06" @default.
- W3016471569 modified "2023-09-23" @default.
- W3016471569 title "GENERALIZED BESSEL AND FRAME MEASURES" @default.
- W3016471569 doi "https://doi.org/10.22190/fumi2001217z" @default.
- W3016471569 hasPublicationYear "2020" @default.
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