In 2012, Găvruţa introduced the notions of K-frame and of atomic system for a linear bounded operator K in a Hilbert space H, in order to decompose its range R(K) with a frame-like expansion. In this article, we revisit these concepts for an unbounded and densely defined operator A: D(A) → H in two different ways. In one case, we consider a non-Bessel sequence where the coefficient sequence depends continuously on f∈ D(A) with respect to the norm of H. In the other case, we consider a Bessel sequence and the coefficient sequence depends continuously on f∈ D(A) with respect to the graph norm of A.

Bellomonte G., Corso R. (2020). Frames and weak frames for unbounded operators. ADVANCES IN COMPUTATIONAL MATHEMATICS, 46(2) [10.1007/s10444-020-09773-3].

Frames and weak frames for unbounded operators

Bellomonte G.;Corso R.
2020-01-01

Abstract

In 2012, Găvruţa introduced the notions of K-frame and of atomic system for a linear bounded operator K in a Hilbert space H, in order to decompose its range R(K) with a frame-like expansion. In this article, we revisit these concepts for an unbounded and densely defined operator A: D(A) → H in two different ways. In one case, we consider a non-Bessel sequence where the coefficient sequence depends continuously on f∈ D(A) with respect to the norm of H. In the other case, we consider a Bessel sequence and the coefficient sequence depends continuously on f∈ D(A) with respect to the graph norm of A.
Settore MAT/05 - Analisi Matematica
Bellomonte G., Corso R. (2020). Frames and weak frames for unbounded operators. ADVANCES IN COMPUTATIONAL MATHEMATICS, 46(2) [10.1007/s10444-020-09773-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/412648
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