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Open AccessArticle

Sums of A Pair of Orthogonal Frames

Department of Mathematical Sciences, Tennessee State University, Nashville, TN 37209, USA
Mathematics 2019, 7(7), 582; https://doi.org/10.3390/math7070582
Received: 9 May 2019 / Revised: 21 June 2019 / Accepted: 24 June 2019 / Published: 29 June 2019
Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also 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. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames. View Full-Text
Keywords: frames; orthogonal frames; canonical dual; alternate dual frames; orthogonal frames; canonical dual; alternate dual
MDPI and ACS Style

Bhatt, G. Sums of A Pair of Orthogonal Frames. Mathematics 2019, 7, 582.

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