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MATHEMATICS AND INFORMATICS*

ANNOUNCEMENT FOR 1999

**Advanced Course on Integral Operators and Related Problems**

Date: 12 - 20 May, 1999

Location: TICMI (Tbilisi)

**Paolo E. Ricci** (University of Rome, "La Sapienca")

ON GENERALIZED ORTHOGONAL POLYNOMIALS OF HYPERGEOMETRIC TYPE.

**Summary:** General theory.
Relativistic orthogonal polynomials (3 hours).

**Paolo E. Ricci** (University of Rome, "La Sapienca")

COMPUTATION OF NEWTON SUM-RULES FOR THE ZEROS OF ORTHOGONAL POLYNOMIALS.

**Summary:**Starting from differential equation. Starting from three-term recurence
relation. Applications (3 hours).

**Paolo E. Ricci** (University of Rome, "La Sapienca")

COMPUTATION OF THE EIGENVALUES OF SECOND KIND FREDHOLM OPERATORS.

**Summary:** Rayleigh-
Ritz and Fichera's orthogonal invariants methods. The inverse iteration method.
Applications (3 hours).

**Dazmir Schulaia** (I. Javakhishvili Tbilisi State University)

LINEAR THEORY OF INTEGRAL EQUATIONS AND THEIR APPLICATIONS.

**Summary:** The lectures
present several topics of the theory of linear integral equations, beginning
with rather elementary expository material and going on to some of the
current developments. Namely, Fredholm theory, theory of singular
integral equations, integral equations with fixed singularities, applications
to the transport theory
(7 hours).

**Advanced Course on Function Spaces and Applications**

Date: 6 - 13 September, 1999

Location: TICMI (Tbilisi)

**Vakhtang Kokilashvili** (Razmadze Mathematical Institute, Georgian Academy of Scinces, Georgia)

NEW ASPECTS IN WEIGHT THEORY

**Summary:** The weight problems have become one of the most dynamically parts of harmonic analysis. Solutions of many important problems have been closely linked with these problems. In the lectures we are going to present a survey of recent results concerning the following problems: Two-weight criteria of boundedness and compactness in Banach function spaces; Criteria of bounded and compact imbeddings of Sobolev (Liouville) space into Lebesque space, generally speaking, with different weights; Two-weight estimates for singular integrals and applications to PDE (5 hours).

**Alois Kufner** (Mathematical Institute, Academy of Scinces, Czech Republic)

HARDY’S INEQUALITY AND RELATED TOPICS

**Summary: **Higher order Hardy inequalities (i.e. containing higher order derivatives) with various types of function classes, among other with overdetermined and underdetermined boundary conditions, with mixed and combined boundary conditions as well as with conditions inside the definition interval. Hardy type inequalities with different norms. Fractional order Hardy inequalities, via interpolation theory as well as direct approaches. More-dimensional analogs of Hardy’s inequality and "multiple" weighted norm inequalities. Application to boundary value problems to linear and nonlinear elliptic operators, in particular, the connection with spectral problems.

**
Coordinator:**
George Jaiani

These course is suitable for advanced graduate students or recent Ph.D.'s. The participants will also have an opportunity to give 20-minute talkes on their own work at a mini-symposium which will take place during the Advanced Course. Lectures and abstracts of the talks will be published and distributed among the lecturers and participants after Advanced Course. The registration fee for participants is 400 USD which includes all local expenses during the Advanced Course. A restricted number of participants will be awarded grants.

**Further information**: TICMI, I.Vekua Institute of Applied Mathematics of
Tbilisi State University, University Str. 2, Tbilisi 380043,
Georgia

e.mail: jaiani@viam.hepi.edu.ge

Tel.:+995 32 305995