Frame Scaling by Graphs

K. Ayyanar (), P. Sam Johnson () and A. Senthil Thilak ()
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K. Ayyanar: National Institute of Technology Karnataka, Surathkal
P. Sam Johnson: National Institute of Technology Karnataka, Surathkal
A. Senthil Thilak: National Institute of Technology Karnataka, Surathkal

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 891-900

Abstract: Abstract In this paper, we investigate the scalability of a given frame in $$\mathbb {R}^n$$ R n by using graphs. For each frame $$\phi $$ ϕ in $$\mathbb {R}^n$$ R n , we associate a simple undirected graph $$G(\phi )$$ G ( ϕ ) and use it to verify the scalability of $$\phi $$ ϕ . We provide some necessary conditions to test the scalability of a given frame. Finally, we study the scalability of some special classes of frames by using graphs.

Keywords: Frame graph; Tight frame; Scalable frame; Scalable graph.; 42C15; 05C50 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00809-2

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