M6150 Functional Analysis I

Faculty of Science
Spring 2012
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 13:00–14:50 M4,01024
  • Timetable of Seminar Groups:
M6150/01: Thu 13:00–13:50 M3,01023, O. Došlý
Prerequisites
M3100 Mathematical Analysis III
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to introduce the bases of the linear functional analysis, namely the theory of infinite dimensional vector spaces and their duals. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Normed linear space, Banach space. Definitions and examples. Unitary and Hilbert spaces. Elements of locally convex topological spaces. 2. Linear operators, examples, space of continuous operators. Open mappings theorem and Hahn-Banach theorem. Continuous linear functionals. 3. Dual spates. Definition and examples. Geometry of linear functionals. Reflexivity, Banach-Steinhaus theorem, weak convergence. 4. Compact operators, elements of spectral theory.
Literature
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2012, recent)
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