Premium
On the existence of exponential polynomials with prefixed gaps
Author(s) -
Mora G.,
Sepulcre J. M.,
Vidal T.
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt043
Subject(s) - mathematics , counterexample , conjecture , closure (psychology) , exponential function , string (physics) , rational number , set (abstract data type) , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , law , mathematical physics , political science , computer science , programming language
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 R P , the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.