On the existence of exponential polynomials with prefixed gaps

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Title: On the existence of exponential polynomials with prefixed gaps
Authors: Mora, Gaspar | Sepulcre, Juan Matias | Vidal, Tomás
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Functions of a complex variable | Entire functions | Fractals
Knowledge Area: Análisis Matemático
Issue Date: 17-Jul-2013
Publisher: London Mathematical Society
Citation: Bulletin of the London Mathematical Society. 2013, 45(6): 1148-1162. doi:10.1112/blms/bdt043
Abstract: This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.
Sponsor: The second author was partially supported by Vicerrectorado de Investigación, Desarrollo e Innovación de la Universidad de Alicante under project GRE11-23.
URI: http://hdl.handle.net/10045/38408
ISSN: 0024-6093 (Print) | 1469-2120 (Online)
DOI: 10.1112/blms/bdt043
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2013 London Mathematical Society
Peer Review: si
Publisher version: http://dx.doi.org/10.1112/blms/bdt043
Appears in Collections:INV - CADAGL - Artículos de Revistas

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