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Sums of A Pair of Orthogonal Frames

Author

Listed:
  • Ghanshyam Bhatt

    (Department of Mathematical Sciences, Tennessee State University, Nashville, TN 37209, USA)

Abstract

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.

Suggested Citation

  • Ghanshyam Bhatt, 2019. "Sums of A Pair of Orthogonal Frames," Mathematics, MDPI, vol. 7(7), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:582-:d:244239
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    Cited by:

    1. Osmin Ferrer & Arley Sierra & Osvaldo Polo, 2022. "Orthogonal Frames in Krein Spaces," Mathematics, MDPI, vol. 10(19), pages 1-15, October.

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