### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 52- |

Numero di pagine | 22 |

Rivista | Axioms |

Volume | 8 |

Stato di pubblicazione | Published - 2019 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory
- Mathematical Physics
- Logic
- Geometry and Topology

### Cita questo

*Axioms*,

*8*, 52-.

**PIP-Space Valued Reproducing Pairs of Measurable Functions.** / Trapani, Camillo; Antoine, Jean-Pierre.

Risultato della ricerca: Article

*Axioms*, vol. 8, pagg. 52-.

}

TY - JOUR

T1 - PIP-Space Valued Reproducing Pairs of Measurable Functions

AU - Trapani, Camillo

AU - Antoine, Jean-Pierre

PY - 2019

Y1 - 2019

N2 - We analyze the notion of reproducing pairs of weakly measurable functions, ageneralization of continuous frames. The aim is to represent elements of an abstract space Y assuperpositions of weakly measurable functions belonging to a space Z := Z(X, m), where (X, m) is ameasure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbertspaces; (ii) Y is a Hilbert space, but Z is a PIP-space; (iii) Y and Z are both PIP-spaces. It is shown, inparticular, that the requirement that a pair of measurable functions be reproducing strongly constrainsthe structure of the initial space Y. Examples are presented for each case.

AB - We analyze the notion of reproducing pairs of weakly measurable functions, ageneralization of continuous frames. The aim is to represent elements of an abstract space Y assuperpositions of weakly measurable functions belonging to a space Z := Z(X, m), where (X, m) is ameasure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbertspaces; (ii) Y is a Hilbert space, but Z is a PIP-space; (iii) Y and Z are both PIP-spaces. It is shown, inparticular, that the requirement that a pair of measurable functions be reproducing strongly constrainsthe structure of the initial space Y. Examples are presented for each case.

UR - http://hdl.handle.net/10447/355144

M3 - Article

VL - 8

SP - 52-

JO - Axioms

JF - Axioms

SN - 2075-1680

ER -