Universal expansions in negative and complex bases.
Komornik, Vilmos, Loreti, Paola (2010)
Integers
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Komornik, Vilmos, Loreti, Paola (2010)
Integers
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Y.-F. S. Pétermann (2010)
Acta Arithmetica
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P. Skibiński (1970)
Annales Polonici Mathematici
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David Färm, Tomas Persson, Jörg Schmeling (2010)
Fundamenta Mathematicae
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We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.
Aleksandar Krapež, M.A. Taylor (1985)
Publications de l'Institut Mathématique
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W. Grabowski, W. Szwarc (1966)
Applicationes Mathematicae
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Pushkin, L. (2002)
Lobachevskii Journal of Mathematics
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Miodrag Rašković (1979)
Publications de l'Institut Mathématique
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W.H. Echols (1893)
Bulletin of the New York Mathematical Society
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G. Grekos, L. Haddad, C. Helou, J. Pihko (2007)
Acta Arithmetica
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Ondrej F. K. Kalenda (2002)
Colloquium Mathematicae
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We prove, among other things, that the space C[0,ω₂] has no countably norming Markushevich basis. This answers a question asked by G. Alexandrov and A. Plichko.
Christoph Schmitt (2006)
Acta Arithmetica
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Zbigniew Ciesielski (2001)
Applicationes Mathematicae
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As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information....
T. V. Narayana, E. Goodman (1969)
Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche
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James R. Holub (1998)
Annales Polonici Mathematici
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E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach...
Luís Roçadas (2003)
Acta Arithmetica
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Goins, Edray Herber (2009)
Integers
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