Kuchmins'ka K. Development of the analytic theory of two-dimensional continued fractions

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0512U000796

Thesis Registration Form

0512U000796.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

25-10-2012

Specialized Academic Board

Д 35.051.18

Ivan Franko National University of Lviv

Essay

The thesis is devoted to development of the analytic theory of a new apparatus for rational approximation of two variable functions, namely two-dimensional continued fractions. In the thesis elementary properties of such fractions have been investigated, the difference formulae of two approximants have been established, and methods for the investigation of their convergence have been developed. Classical criteria of the continued fraction convergence in bounded and unbounded domains have been generalized. The principle of correspondence for continued fractions has been transferred on two-dimensional continued fractions.

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Files

aref.doc

dis.pdf

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