Тригонометричні ряди та канторвали / Trigonometric series and Cantorvals

Abstract: У доповіді буде розглядатися один клас збіжних додатних рядів, члени яких пов'язані з тригонометричними функціями. Залежно від значення початкових параметрів множина неповних сум такого ряду може бути скінченним об'єднанням відрізків, множиною канторівського типу та навіть канторвалом.

In the talk, we consider one class of convergent positive series whose terms are related to trigonometric functions. The set of incomplete sums of such a series may be a finite union of intervals, Cantor-type set, or even Cantorval depending on values of initial parameters.

Ukrainianclassical analysis and ODEsnumber theory

Audience: researchers in the discipline

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Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable

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