For a given positive integer m, let A = {0, 1,...,m} and q is an element of (m,m+1). A sequence (c(i)) = c(1)c(2) ... consisting of elements in A is called an expansion of x if Sigma(infinity)(i=1) c(i)q(-i) = x. It is known that almost every x belonging to the interval [0, m/(q - 1)] has uncountably many expansions. In this paper we study the existence of expansions (d(i)) of x satisfying the inequalities Sigma(n)(i=1) d(i)q(-i) >= Sigma(n)(i=1) c(i)q(-i), n = 1,2,..., for each expansion (c(i)) of x.

OPTIMAL EXPANSIONS IN NON-INTEGER BASES / Karma, Dajani; M., De Vries; Vilmos, Komornik; Loreti, Paola. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 140:2(2012), pp. 437-447. [10.1090/s0002-9939-2011-11226-7]

OPTIMAL EXPANSIONS IN NON-INTEGER BASES

LORETI, Paola
2012

Abstract

For a given positive integer m, let A = {0, 1,...,m} and q is an element of (m,m+1). A sequence (c(i)) = c(1)c(2) ... consisting of elements in A is called an expansion of x if Sigma(infinity)(i=1) c(i)q(-i) = x. It is known that almost every x belonging to the interval [0, m/(q - 1)] has uncountably many expansions. In this paper we study the existence of expansions (d(i)) of x satisfying the inequalities Sigma(n)(i=1) d(i)q(-i) >= Sigma(n)(i=1) c(i)q(-i), n = 1,2,..., for each expansion (c(i)) of x.
2012
beta-expansion; ergodicity; greedy expansion; invariant measure
01 Pubblicazione su rivista::01a Articolo in rivista
OPTIMAL EXPANSIONS IN NON-INTEGER BASES / Karma, Dajani; M., De Vries; Vilmos, Komornik; Loreti, Paola. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 140:2(2012), pp. 437-447. [10.1090/s0002-9939-2011-11226-7]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/402931
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact