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Lecturer(s)
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Course content
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1. Norms on linear spaces, normed spaces 2. Completeness, Banach spaces 3. Examples of normed and Banach spaces 4. Continuous linear mappings, functionals 5. Hahn-Banach theorem and its application 6. Open-mapping theorem and closed-graph theorem 7. Dual normed spaces and their properties 8. Examples of dual spaces 9. Reflexive spaces 10. Hilbert spaces 11. Fourier series in Hilbert spaces
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Normed and Banach spaces, continuity of linear mappings, dual spaces, reflexivity, Hilbert spaces and Fourier series, Hanh-Banach theorem, open mapping theorem, closed-graph theorem.
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Prerequisites
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Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.
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Assessment methods and criteria
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unspecified
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Recommended literature
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Kolgomorov, A. N. a Fomin, S. V. Základy teorie funkcí a funkcionální analýzy. Praha: SNTL, 1975.
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Lukeš, J. Úvod do funkcionální analýzy. Praha: Karolinum, 2011.
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Taylor, A. E. Úvod do funkcionální analýzy. Praha: Academia, 1973.
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