Frame completions with prescribed norms: local minimizers and applications
被引:5
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作者:
Massey, Pedro G.
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机构:
UNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
Consejo Nacl Invest Cient & Tecn, IAM, Buenos Aires, DF, ArgentinaUNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
Massey, Pedro G.
[1
,2
]
Rios, Noelia B.
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机构:
UNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
Consejo Nacl Invest Cient & Tecn, IAM, Buenos Aires, DF, ArgentinaUNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
Rios, Noelia B.
[1
,2
]
Stojanoff, Demetrio
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机构:
UNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
Consejo Nacl Invest Cient & Tecn, IAM, Buenos Aires, DF, ArgentinaUNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
Stojanoff, Demetrio
[1
,2
]
机构:
[1] UNLP, Dept Matemat, FCE, La Plata, Buenos Aires, Argentina
[2] Consejo Nacl Invest Cient & Tecn, IAM, Buenos Aires, DF, Argentina
Let be a finite sequence of vectors in and let be a finite sequence of positive numbers, where for . We consider the completions of of the form obtained by appending a sequence of vectors in such that a(2) = a (i) for , and endow the set of completions with the metric where . In this context we show that local minimizers on the set of completions of a convex potential P (phi) , induced by a strictly convex function phi, are also global minimizers. In case that phi(x) = x (2) then P (phi) 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.
机构:
Univ Siena, Dipartimento Ingn Informaz & Sci Matemat, Via Roma 56, I-53100 Siena, Italy
Abdus Salaam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, ItalyUniv Siena, Dipartimento Ingn Informaz & Sci Matemat, Via Roma 56, I-53100 Siena, Italy
Bellettini, Giovanni
Novaga, Matteo
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机构:
Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, ItalyUniv Siena, Dipartimento Ingn Informaz & Sci Matemat, Via Roma 56, I-53100 Siena, Italy
Novaga, Matteo
Kholmatov, Shokhrukh Yusufovich
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机构:
Abdus Salaam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy
Scuola Int Super Studi Avanzati, Via Bonomea 265, I-34136 Trieste, ItalyUniv Siena, Dipartimento Ingn Informaz & Sci Matemat, Via Roma 56, I-53100 Siena, Italy
机构:
Univ Buenos Aires, Dept Matemat, Fac Ciencias Exactas & Nat, IMAS,CONICET, Pabellon 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, ArgentinaUniv Buenos Aires, Dept Matemat, Fac Ciencias Exactas & Nat, IMAS,CONICET, Pabellon 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina
Heineken, Sigrid B.
Llarena, Juan P.
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机构:
UNSL, CONICET, Inst Matemat Aplicada San Luis, Ejercito Andes 950, RA-5700 San Luis, ArgentinaUniv Buenos Aires, Dept Matemat, Fac Ciencias Exactas & Nat, IMAS,CONICET, Pabellon 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina
Llarena, Juan P.
Morillas, Patricia M.
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机构:
UNSL, CONICET, Inst Matemat Aplicada San Luis, Ejercito Andes 950, RA-5700 San Luis, Argentina
UNSL, FCFMyN, Dept Matemat, Ejercito Andes 950, RA-5700 San Luis, ArgentinaUniv Buenos Aires, Dept Matemat, Fac Ciencias Exactas & Nat, IMAS,CONICET, Pabellon 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina
机构:
Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China
Xu, Zhiqiang
Xu, Zili
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机构:
Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China