Cantorvals as sets of subsums for a series connected with trigonometric functions

Mykola Pratsiovytyi; Dmytro Karvatskyi

paper

Cantorvals as sets of subsums for a series connected with trigonometric functions

arXiv:2308.13521

Abstract

We study properties of the set of subsums for a convergent series $k_{1} sin x + \dots + k_{m} sin x + \dots + k_{1} sin x^{n} + \dots + k_{m} sin x^{n} + \dots$ , where $k_{1}, k_{2}, k_{3}, \dots, k_{m}$ are fixed positive integers and $0 < x < 1$ . Depends on parameter $x$ this set can be a finite union of closed intervals or Cantor-type set or even Cantorval.