PIP-space valued reproducing pairs of measurable functions

Trapani, Camillo;Antoine, Jean-Pierre;Corso, Rosario;et.al.
(2021) Mediterranean Journal of Mathematics — Vol. 18, n° 11, p. 1-20 (2021)

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Authors
  • Trapani, Camillo
    Author
  • Antoine, Jean-Pierreorcid-logoUCLouvain
    Author
  • Corso, Rosario
    Author
  • et. al.
Abstract
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 positiveself-adjoint 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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Trapani, C., Antoine, J.-P., Corso, R., & et al. (2021). PIP-space valued reproducing pairs of measurable functions. Mediterranean Journal of Mathematics, 18(11), 1-20. https://doi.org/10.1007/s00009-020-01652-x (Original work published 2021)