Submitted:
09 May 2019
Posted:
10 May 2019
Read the latest preprint version here
Abstract
A sum of different frames under the action of a bounded linear operator is studied with the help of analysis, synthesis and frame operators. In particular, it is shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. For a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate duals to be orthogonal.
Keywords:
Frames
; Orthogonal frames
; Canonical dual
; Alternate dual
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