IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Frame completions with prescribed norms: local minimizers and applications
Autor/es:
STOJANOFF, DEMETRIO; MASSEY, PEDRO G.; RIOS, NOELIA B.
Revista:
ADVANCES IN COMPUTATIONAL MATHEMATICS
Editorial:
SPRINGER
Referencias:
Año: 2018 vol. 44 p. 51 - 51
ISSN:
1019-7168
Resumen:
Let F0=fi i∈In0 be a finite sequence of vectors in ℂd and let a=(ai)i∈Ik be a finite sequence of positive numbers, where In= 1 , ? , n for n∈ ℕ. We consider the completions of F0 of the form F= (F0, G) obtained by appending a sequence G=gi i∈Ik of vectors in ℂd such that ∥gi∥2 = ai for i∈ Ik, and endow the set of completions with the metric d(F,F~)=max{∥gi−g~i∥:i∈Ik} where F~=(F0,G~). In this context we show that local minimizers on the set of completions of a convex potential Pφ, induced by a strictly convex function φ, are also global minimizers. In case that φ(x) = x2 then Pφ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn?s conjecture on the FOD.