1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: To explain basic results on normed spaces, in particular, on Banach and Hilbert spaces.

COURSE DESCRIPTION AND SYLLABUS:
1. Inner product and normed spaces. Subspaces. Convexity
2. Examples of Hilbert spaces: l2 and L2. Orthonormal basis, Bessel inequality, Parseval equality, Fourier expansion.
3. Minkowski and Holder inequalities. lp and Lp spaces. Bases.
4. Completions of normed spaces. Factor spaces.
5. Best approximation. Riesz theorem. Bounded linear functionals.
6. Dual spaces. Hahn-Banach theorem and its consequences.
7. Reflexive spaces.
8. Weak topologies.

1. Funkcionalna analiza, S. Kurepa, Školska knjiga, Zagreb, 1981.
2. Functional analysis, G. Bachman, L. Narici, Academic Press, 1966.
3. A Hilbert space problem book, P. R. Halmos, Van Nostrand, 1967.
4. Analysis NOW, G. K. Pedersen, Springer Verlag, 1998.

Mandatory course - Regular study - Theoretical Mathematics