# Department of Functional Analysis and its Applications

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## You are here

# Department of Functional Analysis and its Applications

Head of the department: Moiseev Evgeny, Academician of RAS, Professor, Dr. Sc., Dean of the Faculty CMC MSU

Contact information

E-mail:

[fa@cs.msu.su](mailto:fa@cs.msu.su)

Phone number:

+7 (495) 939-08-36

Other contact information

Address:

119991, Moscow, GSP-1, Leninskiye Gory, MSU, 2nd Educational Building, CMC Faculty, room 796 (Head of the department)

The Department was founded in 2008. Main topics are: boundary value and spectral problems for PDEs of elliptic and mixed type, spectral analysis, boundary control problems for oscillating processes, linear integral equations, completeness and basis properties of functional systems.

Students of the Department attend a special pro-seminar on functional analysis.

### Staff members:

- Kapustin Nikolay, Professor, Dr. Sc.
- Polosin Alexey, Associated Professor, PhD, Scientific Secretary of the Department
- Kholomeeva Anna, Assistant Professor, PhD
- Gulyaev Denis, Assistant Professor, PhD

### Regular courses:

- Functional Analysis by Prof. Moiseev, 64 hours, 5th semester.
- Functional Analysis by Prof. Moiseev, 32 hours, 6th semester.
- Functional Analysis by Assoc. Prof. Kapustin, 32 hours, 5th semester.
- Functional Analysis by Assoc. Prof. Kapustin, 32 hours, 7th semester.
- Mathematical Analysis by Assoc. Prof. Polosin, 64 hours, 2nd semester.
- Mathematical Analysis by Assoc. Prof. Polosin, 64 hours, 3rd semester.

### Special courses:

- Methods for Solving Integral Equations by Assoc. Prof. Polosin, 32 hours, 5th semester.

### Special scientific seminars:

- Spectral Theory of Differential Operators and Actual Problems of Mathematical Physics by Prof. Moiseev and Prof. Il'in.
- Boundary Value and Spectral Problems by Prof. Moiseev.

## Main Scientific Directions

### Boundary value problems for mixed type equations

(Prof. E.I. Moiseev)

Fundamental results on representing solutions to boundary value problems in the form of biorthogonal series have been obtained in the spectral theory. To justify the obtained expansions, important theorems on completeness and basis properties of appropriate systems of root functions have been proved.

The method of integral equations (especially singular ones) is another powerful tool to explore boundary value problems. Using this method, many non-classical problems have been successfully investigated.

Location of the spectrum for non-self-adjoint problems, in particular, problems with non-local boundary conditions or oblique derivative problems, is of special interest. In this sphere, important results on spectrum's location, on its belonging to the Carleman parabola and on various properties of root functions have been obtained.

### Boundary control problems for oscillating processes

(Prof. E.I. Moiseev)

This field, which is being developed in the close cooperation with the team of the Department of General Mathematics, dwells upon boundary value problems for optimal control of oscillating processes. In particular, for a large time interval, which is a multiple of the string length, the optimal boundary control of string oscillations has been found for various problems of the first, second and third kind, in terms of generalized solutions to the wave equation which have a uniformly finite energy.\
Recent papers:

1. E.I.Moiseev and V.E.Ambartsumyan, On the basis property of eigenfunctions of the Frankl problem with a nonlocal oddness condition of the second kind // Integral Transforms and Special Functions, vol. 21, no. 10, pp. 745-754, 2010.
2. E.I.Moiseev and V.E.Ambartsumyan, On the solvability of nonlocal boundary value problem for the Helmholtz equation with the equality of flows at the part of the boundary and its conjugated problem // Integral Transforms and Special Functions, vol. 21, no. 12, 2010.

### Recent publications:

• 2013

1. Moiseev E.I., Nefedov P.V. Frankl problem for the Lavrent'ev-Bitsadze equation in a 3D-domain // Integral Transforms and Special Functions. 2013. 24. N 7. P. 554-560.

• 2012

1. Kapustin N.Yu. On the spectral problem arising in the solution of a mixed problem for the heat equation with a mixed derivative in the boundary condition // Differential Equations. 2012. 48. N 5. P. 701-706.
2. Moiseev E.I., Kholomeeva A.A. Optimal boundary control by displacement at one end of a string under a given elastic force at the other end // Proc. of the Steklov Inst. of Math. 2012. 276. N 1. P. 153-160.
3. Moiseev E.I., Kholomeeva A.A. Optimization of the boundary control of string vibrations at one string end with a given mode at the other end // Doklady Mathematics. 2012. 86. N 1. P. 454-456.
4. Moiseev E.I., Likhomanenko T.N. A nonlocal boundary value problem for the Lavrent’ev-Bitsadze equation // Doklady Mathematics. 2012. 86. N 2. P. 635-637.

## News

20 November 2019

[International Russian-French workshop "Actual problems of artificial intelligence"](https://cs.msu.ru/en/news/3101)

31 May 2019

[Международный научный семинар “Advanced Light Scattering Techniques”](https://cs.msu.ru/en/news/2997)

19 December 2018

[International Workshop "New Approaches in Computer-Assisted Translation: case of Talmud"](https://cs.msu.ru/en/news/2935)

18 December 2018

[CMC MSU – Zhejiang international workshop](https://cs.msu.ru/en/news/2933)

18 December 2018

[Russian-Chinese academic and research cooperation workshop](https://cs.msu.ru/en/news/2932)

16 May 2017

[ISPRS International Workshop — PSBB17](https://cs.msu.ru/en/news/2616)

26 October 2016

[MSU-Huawei Joint Workshop](https://cs.msu.ru/en/news/2464)

06 September 2016

[CMC MSU-Huawei International Workshop "Selected topics in multimedia image processing and analysis"](https://cs.msu.ru/en/news/2408)

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## Events

13 October 2025 to 17 October 2025

[XXXVII International Seminar on Stability Problems for Stochastic Models](https://cs.msu.ru/en/news/4279)

29 October 2024 to 31 October 2024

[The 5th International Science and Technology Conference «Modern Network Technologies, MoNeTec-2024»](https://cs.msu.ru/en/news/4066)

20 November 2022

[Virtual Open Day for International Students at Lomonosov Moscow State University](https://cs.msu.ru/en/news/3788)

27 October 2022 to 29 October 2022

[4th International Science and Technology Conference «Modern Network Technologies, MoNeTec - 2022»](https://cs.msu.ru/en/news/3675)

05 October 2022

[MSU Open Day for Exchange Students](https://cs.msu.ru/en/news/3760)

22 May 2022

[Virtual Open Day for International Applicants at Lomonosov Moscow State University](https://cs.msu.ru/en/news/3706)

20 February 2022

[Virtual Open Day for International Students at Lomonosov Moscow State University on February 20, 2022](https://cs.msu.ru/en/news/3636)

16 February 2022

[Ярмарка вакансий для студентов и выпускников МГУ](https://cs.msu.ru/en/news/3649)

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