Continuous frames for unbounded operators

2019/12/30 by Bellomonte, Giorgia
#41A65 #42C15 #47A05 #47A63 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1912.13097

Abstract

Few years ago Găvruţa gave the notions of K-frame and atomic system for a linear bounded operator K in a Hilbert space H in order to decompose R(K), the range of K, with a frame-like expansion. These notions are here generalized to the case of a densely defined and possibly unbounded operator on a Hilbert space A in a continuous setting, thus extending what have been done in a previous paper in a discrete framework.

Related

• Continuous k-frames and their duals
• Continuous generalized atomic subspaces for operators in Hilbert spaces
• Construction of Continuous Frames in Hilbert spaces
• Fusion frames for operators and atomic systems
• Some results of K-frames and their multipliers