Towards Generalized Riesz Systems Theory

Kamuda, Alan; Kużel, Sergiusz

doi:10.48550/arxiv.1910.07606

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Transforming Functions Into Frames By Metric Operators1

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2020

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“…We will consider more examples (concerning, in particular, lower semi-frames) in the next section. As an immediate consequence of Theorem 6.1 we get the following result (compare with [25,Corollary II.1]). We recall that two sequences {φ n } n∈N , {ψ n } n∈N are said bi-orthogonal if ψ n |φ m = δ n,m , the Kronecker symbol.…”

Section: Transforming Functions Into Frames By Metric Operatorsmentioning

confidence: 60%

Lower semi-frames and metric operators

Antoine¹,

Corso²,

Trapani³

2020

Preprint

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This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive selfadjoint operator. A necessary condition is that the domain of the analysis operator associated to the function be dense. The study is done also with the help of the generalized frame operator associated to a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.

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Section: Transforming Functions Into Frames By Metric Operatorsmentioning

confidence: 60%