témavezető: Kroó András
helyszín (magyar oldal): Department of Analysis, Institute of Mathematics, BME helyszín rövidítés: BME
A kutatási téma leírása:
The main goal of this PhD Programme is to introduce the students to the main topics and methods of the Constructive Function Theory and Approximation Theory. By the completion of the course the students are enabled to conduct independent study and research in fields touching on the topics of the course. They also learn how to use these methods to solve specific problems. In addition, the students develop some special expertise in the Constructive Function
Theory, which they can use efficiently in other mathematical fields, and in applications, as well.
The main topics covered by this PhD Programme are as follows:
1. Classical polynomial inequalities (Bernstein, Markov, Remez, Schur, Nikolskii inequalities).
2. Approximation by linear operators. Fourier and Fej´er operators, Bernstein Polynomials, positive linear operators. Korovkin theorem.
3. Lacunary polynomial approximation, incomplete polynomials, M¨untz type theorems.
4. Bernstein-Markov type inequalities for multivariate polynomials on convex and star like domains in uniform and integral norms.
5. Markov type inequalities for homogeneous polynomials on convex bodies and Tangential Bernstein-Markov type inequalities.
6. Remez type inequalities for multivariate polynomials on star like domains and convex bodies and their application.
7. Admissible and optimal meshes for multivariate polynomials.
8. Approximation by ridge functions and incomplete polynomials in several variables.
9. Weierstrass type theorems for approximation by homogeneous polynomials on the boundary of convex domains.
10. Approximation of convex bodies by convex algebraic level surfaces.
előírt nyelvtudás: English felvehető hallgatók száma: 1
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