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Further results on the connectivity of Parseval frame wavelets
Authors:
G. Garrigós, E. Hernández, H. Sikic and F. Soria
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3211-3221
MSC (2000):
Primary 42C15, 42C40
Posted:
May 11, 2006
MathSciNet review:
2231904
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Abstract: In a previous paper, the authors introduced new ideas to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.
References
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J. Cilleruelo and A. Córdoba, La teoría de los números. Mondadori España (1992).
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G. Garrigós, E. Hernández, H. Šikic, F. Soria, G. Weiss and E. Wilson, ``Connectivity in the set of Tight Frame Wavelets''. Glasnik Matematicki. 38 (58) (2003), 75-98. MR 1987107 (2005g:42078)
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Additional Information
G. Garrigós
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email:
gustavo.garrigos@uam.es
E. Hernández
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email:
eugenio.hernandez@uam.es
H. Sikic
Affiliation:
Department of Mathematics, University of Zagreb, Bijeni\u{c}ka 30, 10000 Zagreb, Croatia
Email:
hsikic@math.hr
F. Soria
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email:
fernando.soria@uam.es
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08358-4
PII:
S 0002-9939(06)08358-4
Keywords:
Connectivity,
tight frames,
Parseval frames
Received by editor(s):
January 24, 2005
Received by editor(s) in revised form:
May 12, 2005
Posted:
May 11, 2006
Additional Notes:
The first, second and fourth authors were supported by grant MTM2004-0678, MEC (Spain). The third author was supported by grants MZOS 0037118 (Croatia) and USA-Croatia NSF INT-0245238. The first author was also supported by \emph{Programa Ramón y Cajal, 2001}, MCyT (Spain).
Communicated by:
David R. Larson
Article copyright:
© Copyright 2006 American Mathematical Society
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