Infopaket

Functional analysis

Обов’язкова дисципліна для ОП

First

2022/2023

4 Semester

4

LO 18. Efficiently communicate with the supply of information, ideas, problems and solutions with specialists and support

To successfully learn the discipline “Functional analysis” the student should satisfy the following requirements. They have successfully passed the courses “Calculus”. They know (a) fundamentals of Calculus. They can (a) solve problems of Calculus. They should be able to (a) seek information in the Internet.

Block 1. Spaces Topological structures Методи введення топології Неперервні відображення і гомеоморфізми Компактність Метричні простори Повні метричні простори Лінійні простори Нормовані простори Test work Block 2. Operator theory Space of linear bounded operators Uniform boundedness principle Open mapping principle Euclidean spaces Hilbert space Isomorphism theorem Test work 2 h.

1. Aleksandrian R.A., Mirzakhanian E.A. Obshchaia topologiia. - M.:Vysshaia shkola, 1979. - 336 s. 2. Arkhangel-skii A. V., Ponomarev V. I. Osnovy obshchei topologii v zadachakh i uprazhneniiakh. – M., 1974; 3. Berezanskii Iu.M., G.F.Us, Sheftel- Z.G. Funktsional-nyi analiz. - K.: Vishcha shkola, 1990. - 600 s. 4. Vulikh B.Z. Vvedenie v funktsional-nyi analiz. - M.: Nauka, 1967. - 416 s. 5. Kantorovich L.V., Akilov G.P. Funktsional-nyi analiz. - M.: Nauka, 1984. - 752 s. 6. Kliushin D.A., Semenov V.V. Zadachі ta vpravi z kursu “Funktsіonal-nii analіz”. Elementi zagal-noї topologії. – K.: Vidavnicho-polіgrafіchnii tsentr "Kiїvs-kii unіversitet", 2005. – 67 s. 7. Kliushin D.A., Semenov V.V. Zadachі ta vpravi z kursu “Funktsіonal-nii analіz”. Lіnіinі normovanі prostori ta lіnіinі neperervnі funktsіonali. – K.: Vidavnicho-polіgrafіchnii tsentr "Kiїvs-kii unіversitet", 2006. – 39 s.

Lectures, seminars, independent work, recommended literature processing, homework.

Intermediate assessment: The maximal number of available points is 60. Test work no. 1: RN 1.1, RN 1.2 – 30/18 points. Test work no. 2: RN 1.1, RN 1.2 – 30/18 points. Final assessment (in the form of exam): The maximal number of available points is 40. The results of study to be assessed are RN 1.1, RN 1.2, RN 2.1, and RN 3.1. The form of exam: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).

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