SUBJECT
Title
Topics in analysis
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
2+2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Hausdorff measure and Hausdorff dimension. The Hausdorff dimension of Rn and some fractals, length and 1-dimensional measure.
Haar measure. Existence and uniqueness.
Approximation theory. Approximation with Fejér means, de la Vallée Poussin operator, Fejér-Hermite interpolation, Bernstein polynom.
The order of approximation. Approximation with analytic functions.
Approximation with polynomials. Tschebishev polynomials.
Readings
- P. Halmos: Measure Theory, Van Nostrand, 1950
- K.J. Falconer: The Geometry of Fractal Sets, CUP, 1985
- D. Jackson: The theory of approximation, AMS, 1994.