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Frames associated with measurable spaces. (English) Zbl 1033.42036
The paper deals with extensions of results for discrete frames to the setting of continuous frames. Characterizations of continuous frames are derived, as well as conditions for two continuous frames to be similar. Furthermore, a dilation-type result for continuous frames is proved: it states that a continuous frame is a projection of a “Riesz-type frame” for a larger space. Finally, a perturbation result by Casazza and Christensen is generalized to the continuous setting.

42C40Wavelets and other special systems
42C15General harmonic expansions, frames