Dr. Izhar Oppenheim

Time and Place:

  • יום ב 14:00 - 12:00
  • יום ד 10:00 - 08:00

Course topics

Metric and normed spaces. Equivalence of norms in finite dimensional spaces, the Heine-Borel theorem. Convergence of sequences and series of functions: pointwise, uniform, in other norms. Term-by-term differentiation and integration of series of functions, application to power series. Completeness: completeness of the space of continuous functions on a closed interval and a compact metric space. The Weierstrass M-test. The Baire category theorem and applications, bounded linear functionals and the Banach-Steinhaus theorem. Compactness in function spaces and the Arzela-Ascoli theorem. Introduction to Fourier series: Cesaro means, convolutions and Fejer’s theorem. The Weierstrass approximation theorem. L^2 convergence. Pointwise convergence, the Dirichlet kernel and Dini’s criterion.

University course catalogue: 201.1.1051