Normed spaces

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Code:	45582
ECTS:	5.0
Lecturers in charge:	izv. prof. dr. sc. Ilja Gogić
Lecturers:	izv. prof. dr. sc. Ilja Gogić - Exercises
English level: 1,0,0	All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

Load:

1. komponenta

Lecture type Total

Lectures 30

Exercises 15

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

Description:

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.

Literature:

1. semester

Mandatory course - Regular study - Theoretical Mathematics

Consultations schedule:

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Link to the course web page: https://web.math.pmf.unizg.hr/nastava/np/

Link to the notices web page: http://www.pmf.unizg.hr/math/predmet/norpro

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Normed spaces

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