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EnglishIn this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate conditions for them to constitute a ”continuous basis” for the smallest space D of a rigged Hilbert space. This analysis requires suitable extensions of familiar notions as those of frames, Riesz bases and orthonormal bases. A motivation for this study comes from the Gel’fand–Maurin theorem which states, under certain conditions, the existence of a family of generalized eigenvectors of an essentially self-adjoint operator on a domain D which acts like an orthonormal basis of the Hilbert space H. The corresponding object will be called here a Gel’fand distribution basis. The main results are obtained in terms of properties of a conveniently defined synthesis operator
Trapani C., Triolo S., & Tschinke F. (2019). Distribution Frames and Bases. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25(4), 2109-2140.
| Data di pubblicazione: | 2019 |
| Titolo: | Distribution Frames and Bases |
| Autori: | TSCHINKE, Francesco (Corresponding) |
| Citazione: | Trapani C., Triolo S., & Tschinke F. (2019). Distribution Frames and Bases. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25(4), 2109-2140. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00041-018-09659-5 |
| Abstract: | In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate conditions for them to constitute a ”continuous basis” for the smallest space D of a rigged Hilbert space. This analysis requires suitable extensions of familiar notions as those of frames, Riesz bases and orthonormal bases. A motivation for this study comes from the Gel’fand–Maurin theorem which states, under certain conditions, the existence of a family of generalized eigenvectors of an essentially self-adjoint operator on a domain D which acts like an orthonormal basis of the Hilbert space H. The corresponding object will be called here a Gel’fand distribution basis. The main results are obtained in terms of properties of a conveniently defined synthesis operator |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| TschinkeTrioloTrapani.pdf | articolo | Post-print | Open Access Visualizza/Apri | |
| trapani2019 (1).pdf | articolo | Versione Editoriale | Administrator Richiedi una copia |
http://hdl.handle.net/10447/371264
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