# Scientific studies

*Dr. Alexander Goncharov*

## Research interests

Structure theory of locally convex spaces. Basis problem. Properties of bases

Spaces of infinitely differentiable and Whitney functions. Extension operators

Theory of approximation. Extremal polynomials. Lebesgue constants

Complex dynamics. Metric and topological properties of the generalized Julia sets

Orthogonal polynomials for continuous singular measures. Widom factors

Potential theory. Harmonic measures on small sets. Smoothness of Green functions

## Key publications

1. Goncharov A. **On the absence of stability of bases in some Frechet spaces**, *Analysis Mathematica*, V. 46, P. 761-768, 2020. [Download], [Link]

2. Goncharov A., Ural Z. **Mityagin's extension problem. Progress report**, *Journal of Mathematical Analysis and Applications*, V. 448, I. 1, P. 357-375, 2017. [Download], [Link]

3. Alpan G., Goncharov A. **Orthogonal polynomials for the weakly equilibrium Cantor sets**, *Proceedings of the American Mathematical Society*, V. 144, P. 3781-3795, 2016. [Download], [Link]

4. Goncharov A. Hatinoglu B. **Widom factors**, *Potential Analysis*, V. 42, P. 671-680, 2015. [Download], [Link]

5. Goncharov A. **Weakly equilibrium Cantor-type sets**, *Potential Analysis*, V. 40, P. 143-161, 2014. [Download], [Link]

6. Goncharov A. **Bases in the spaces of C**^{oo}-functions on Cantor-type sets, *Constructive Approximation*, V. 23, P. 351-360, 2006. [Download], [Link]

7. Goncharov A. **Perfect sets of finite class without the extension property**, *Studia Mathematica*, V. 126, I. 2, P. 161-170, 1997. [Download], [Link]

8. Goncharov A. **A compact set without Markov's property but with an extension operator for C**^{oo}-functions, *Studia Mathematica*, V. 119, I. 1, P. 27-35, 1996. [Download], [Link]

## Department Seminar

The **Analysis Seminar** at the Department of Mathematics, Bilkent University

## Talks and lectures

Contributions to conferences and invited lectures

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