Displaying similar documents to “The inner periodic structure of a function.”

Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function

Yuji Kodama, Shigeki Matsutani, Emma Previato (2013)

Annales de l’institut Fourier

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A lattice model with exponential interaction, was proposed and integrated by M. Toda in the 1960s; it was then extensively studied as one of the completely integrable (differential-difference) equations by algebro-geometric methods, which produced both quasi-periodic solutions in terms of theta functions of hyperelliptic curves and periodic solutions defined on suitable Jacobians by the Lax-pair method. In this work, we revisit Toda’s original approach to give solutions of the Toda lattice...

Quasicrystals and almost periodic functions

Mariusz Zając (1999)

Annales Polonici Mathematici

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We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.

Approximation of almost periodic functions by periodic ones

Alexander Fischer (1998)

Czechoslovak Mathematical Journal

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It is not the purpose of this paper to construct approximations but to establish a class of almost periodic functions which can be approximated, with an arbitrarily prescribed accuracy, by continuous periodic functions uniformly on ℝ = ( - ∞ ; + ∞ ) .

On some general almost periodic optimal control problems : links with periodic problems and necessary conditions

Denis Pennequin (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed...