Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of domain and boundedness are given. The case of Riesz distribution bases is examined in order to develop a symbolic calculus.
Corso, R., Tschinke, F. (2020). Some notes about distribution frame multipliers. In P. Boggiatto, T. Bruno, E. Cordero, H.G. Feichtinger, F. Nicola, A. Oliaro, et al. (a cura di), Landscapes of Time-Frequency Analysis, Vol.2 (pp. 103-122). Birkhäuser [10.1007/978-3-030-56005-8_6].
Some notes about distribution frame multipliers
Corso, Rosario
;Tschinke, Francesco
2020-01-01
Abstract
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of domain and boundedness are given. The case of Riesz distribution bases is examined in order to develop a symbolic calculus.
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