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EnglishIn 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).
| Data di pubblicazione: | 2020 |
| Titolo: | Frames and weak frames for unbounded operators |
| Autori: | |
| Citazione: | Bellomonte G., & Corso R. (2020). Frames and weak frames for unbounded operators. ADVANCES IN COMPUTATIONAL MATHEMATICS, 46(2). |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10444-020-09773-3 |
| 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 Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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|---|---|---|---|---|
| 10.1007@s10444-020-09773-3.pdf | articolo principale | Versione Editoriale | Administrator Richiedi una copia |
http://hdl.handle.net/10447/412648
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