عنوان مجله
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Iranian Journal of Science and Technology-Transactions of Electrical Engineering
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چکیده
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The conditions for sequences ffkg1
k¼1 and fgkg1
k¼1 being Bessel sequences, frames or Riesz bases, can be expressed in terms
of the so-called cross-Gram matrix. In this paper, we investigate the cross-Gram operator G, associated to the sequence
fhfk; gjig1
j;k¼1 and sufficient and necessary conditions for boundedness, invertibility, compactness and positivity of this
operator are determined depending on the associated sequences. We show that invertibility of G is not possible when the
associated sequences are frames but not Riesz Bases or at most one of them is Riesz basis. In the special case, we prove that
G is a positive operator when fgkg1
k¼1 is the canonical dual of ffkg1
k¼1.
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