Head of the Department
Professor Semyon R. Nasyrov
Tel.: (007843) 2315160
Email: SNasyrov@ksu.ru


Department of Mathematical Analysis
The Department of Mathematical Analysis was founded in 1934. For forty years (19341974) the Department was headed
by the Honoured Scientist of Russian Federation, Professor, Doctor of Science Boris M. Gagayev (18971975),
then (19741998) by Anatolii N. Sherstnyov, Honoured Scientist of the Republic of Tatarstan, Professor, Doctor of Science.
Now the Department is headed by Semen R. Nasyrov, Professor, Doctor of Science.
Staff
General courses taught at the Department for the whole Institute of Mathematics and Mechanics include "Mathematical Analysis", "Functional Analysis and Integral Equations", "Theory of Probability and Mathematical Statistics". In addition, for students of Mechanics, the general course "Theory of Functions of Complex Variable" is read.
In the abovementioned courses, the following manuals and guides
written by our staff are used:
 L.A.Aksent'yev
Problems on Theory of Functions of Complex Variable and Operational
Calculus.
Kazan University Press, (2nd edition), 1984.
 L.A.Aksent'yev
Complex Potential of the Flat Field
.
Kazan University Press, 1989.
 A.N.Sherstnyov
The Guide of Lectures on Mathematical Analysis,
(2nd edition), Kazan University Press, 1993.(Sub title of the
Committee for Higher School at Ministry of Science and Technology
Politics of RF).
 A.N.Sherstnyov
Elements of Measure Theory and the Lebesgue Integral
, Kazan University Press,
1993.
Specialization:
The Chair graduates students in two specializations:
"Functional Analysis" and "Geometrical Theory of
Functions".
The students who choose our Chair for their specialization
start to be involved in the Chair's scientific problems from very early steps
in their university courses. They participate in the seminar "Additional Chapters of Analysis", where they can prepare themselves to
their specialization in two years.
Afterwards,
already within the frameworks of their chosen specialty, they assist in a
cycle of interconnected special courses, which lead them to
the contemporaneous fundamental problems of the modern Functional Analysis
and Theory of Functions. In a number of cases, the Chair forms
specialists along personalized individual Curriculum, provided that the main
special courses in the Curriculum of a specialization are treated in a
specific way.
Specialization "Functional Analysis"
This specialization was opened in 1974 on the basis of the
scientific seminar
"Operator Algebras and their Applications" (supervisor  Honoured Scientist of RT, professor
A.N.Sherstnyov
). Mathematical problems, which led to this specialization, are related to
an intensively developed branch of Functional Analysis, namely
"Topological Algebras and Their Representations".
Active interest on this domain is based on rich achievements in this area;
on the other hand,
topological algebras and their representations constitute a
powerful tool in contemporaneous Mathematical Physics.
One of the central problems of the theory of topological
algebras is the construction of an integration theory there.
The objective of the specialization is a fundamental preparation
of specialists in functional analysis.
An active interest to this part of Mathematical Analysis is
conditioned, on one hand, by large fruitful achievements in the
last few years. On the other hand, it is also due to the importance of
topological algebras and their representations in the capacity
of tools in the mathematical part of modern mathematical
physics. One of central problems of the theory of topological
algebras is a construction of a general integration theory in these
algebras. The objective of the specialization is a fundamental
preparation of specialists in the functional analysis, who must
posses a free command in mentioned domain.
Members of the Chair, who actively work in this domain, lecture a
series of special courses which form the basis of
this specialization.
Graduates who continue along the same specialization in postgraduate
courses as the Chair often work in scientific R&D institutions.
Within the framework of this specialization one can encounter the following
special courses:
 Elementary theory of Hilbert spaces (36 hours).
 Vector spaces (special seminar) (36 hours).
 Banach algebras and their representations (34 hours)
 Finitedimensional operator algebras (special seminar).
 Spectral theorem (54 hours)
 Glisson theorem (special seminar) (36 hours).
 Topological vector spaces (special seminar)(36 hours).
 Elementary theory of von Neumann algebras (68 hours).
 Theory of TomitoTakesaki (32 hours).
Methodical publications for these courses:
 G.D.Lugovaya, Elementary theory of Hilbert spaces,
Kazan University Press, 1985.
 F.F.Sultanbekov, Finitedimensional operator algebras ,
Kazan university Press, 1986.
 N.V.Trunov, Spectral theorem, Kazan University Press,
1989.
 A.N.Sherstnyov, Vector spaces, 1994 (electronic
version appr. 33KB).
 A.N.Sherstnyov, Banach algebras and their
representations, Kazan University Press,
1984.
 A.N.Sherstnyov, Elementary theory of von Neumann
algebras, Kazan University Press, 1988.
Specialization "Geometric Theory of Functions
of Complex Variable"
This specialization was founded early in the 70's on the basis of an existing
scientific seminar "Geometric Theory of
Functions" (supervisor Honoured scientists of RT,
Prof. L.A.Aksent'yev).
Problems connected to specialization were based
on ideas and results by S.N.Andrianov, F.D.Gakhov, M.T.Nuzhin, and G.G.Tumashev. This
specialization combines preparation of students for work on
modern theoretic problems (fine problems of conformal mappings,
Teichmuller spaces) with application to the theory of boundary
value problems in concrete problems of the mechanics of continuous
media. Modern theoretical methods for solving applied
problems supply to graduates in this specialization an ample
field of applications of their knowledge in both scientific
research and production. This specialization was opened on Chair
in 1978. Members of Chair actively work in the domain of
the geometrical theory of functions of complex variable
and lecture on a series of special courses which form a basis of this specialization.
Within its framework the following special courses are read:
 Symmetry method (36 hours)
 Application of the symmetry method to conformal mappings
and boundary value problems (34 hours)
 Geometrical theory of functions of complex variable (70 hours)
 Boundary value problems for analytic functions (54 hours)
 Riemann surfaces and quasiconformal mappings (54 hours)
 Inverse boundary value problems (special seminar) (70 hours)
 Univalent resolvability of boundary value problems
(special seminar) (34 hours)
 Boundary value problems of the mechanics of continuous media
(special seminar) (36 hours)
 Complex potential of a flat field with elements of mathematics
modeling (special seminar) (70 hours)
Methodical publications:
 L.A.Aksent'yev, Symmetry Method, Kazan University Press,
1991.
 L.A.Aksent'yev, Application of symmetry method
to conformal mappings and to boundary value problems, Kazan University
Press, 1993.
Research and Investigation
 Univalent resolvability and wellposedness
of inverse boundary value problems with applications to hydromechanics
 Methods of the functional analysis: Stochastic
structures of the functional analysis
 Construction of measures and integrals
on topological algebraical and order structures
Scientific seminars
 Operator algebras and their applications.
 Geometrical theory of functions.
