He was assistant professor in Differential and Integral Calculus at
Sofia University in the period 1920-1922. In 1922 he became an
associate professor of algebra. Since 1925 till 1928 he was an
extraordinary professor. In 1928 he became a full professor. Since
1928 till his death in 1963 he was a Chairman of the Algebra
Department at Sofia University.
Nikola Obrechkoff became a regular member of the Bulgarian Academy
of Sciences in 1945. Since 1951 he was Director of the Mathematical
Institute.
Obrechkoff was giving lectures in Algebra, Probability Theory,
Summability of Divergent Series, Number Theory. He was a visiting
professor at the universities of Hamburg, Berlin, Geneva, Rome,
Palermo, Leipzig, Dresden, and other.
He has written more than 240 scientific research papers covering a
wide range of Mathematical Analysis, as well as in Algebra, Number
Theory, Statistics and Probability, Mechanics, Numerical Analysis.
He was a master of Classical Analysis with a profound contribution
to the Theory of Divergent Series, one of the best specialists on
the Distribution of Zeros of Algebraic Polynomials, and Summability
of Divergent Series. Author of books on Algebra, Probability, Number
Theory. Author of the monography ``Zeros of Polynomials'', published
by the Bulgarian Academy of Sciences, and ``Verteilung und
Berechnung der Nullstellen reeller Polynome'', published by the
German Academy of Sciences. This work was highly evaluated by
scientists. I. Schoenberg described it as ``the wonderful
presentation''.
Obrechkoff became famous in the scientific world after his
interesting generalization of the classical Descartes' rule of sign
about estimating the number of positive roots of algebraic equations
that he developed and extended to the case of complex roots.
He studied and offered new integral transformations that became a
focus of interest later. Obrechkoff suggested an interesting
extension of the classical Taylor's formula, from where he derived
an explicit interpolation quadrature formula with two nodes. He
obtained sharp estimates for the derivatives of functions defined on
infinite intervals on the real line.
He wrote a number of remarkable papers on summability of divergent
series. He studied and introduced a new method of summability. He
even solved the problem of summability by arithmetic means of the
derivative of Fourier series. He established Tauberian type theorems
for series with gaps.
His works cover a wide range of mathematical fields. Obrechkoff
suggested numerical methods for solving algebraic equations; in the
Probability Theory he offered a new approach in studying the
discrete time Markov chains; he also studied the asymptotic behavior
of classical orthogonal polynomials, he proved the Descartes' rule
for series of orthogonal polynomials; as well as he studied the
expansion of analytic functions with respect to bi-orthogonal
systems. He was active in research till the end of his life.
When he was sixty years of age, Obrechkoff made a significant
discovery in Diophantine Analysis - he solved a problem that had
been open for 50 years. In fact, he proved that Borel's constant in
the approximation of linear forms is equal to 1.
Nikola Obrechkoff participated in many international conferences and
congresses in mathematics - in Oslo (1936), Edinburgh (1958),
Stockholm (1962).
He was a honorable laureate of the most prestigious state awards in
science and culture.
Among his followers have been Acad. Lubomir Iliev, Acad. Blagovest
Sendov, Prof. Petar Rusev, Assoc. Prof. Kiril Dochev.
