Baranovskyi O. Metric and probabilistic theory of numbers defined by the first Ostrogradsky series

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0407U001847

Thesis Registration Form

0407U001847.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

24-04-2007

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The thesis is devoted to the investigation of mathematical objects (fractal sets, singular measures, nondifferentiable functions) with complicated local structure defined in terms of the first Ostrogradsky series. We study some classes of closed nowhere dense sets defined by conditions on elements of their Ostrogradsky series. We found conditions for these sets to be of zero resp. positive Lebesgue measure. We stress the fundamental difference between the metric theory of continued fractions and the Ostrogradsky series.

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Files

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thesis.pdf

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