4th International Conference “Analytical Methods of Analysis and Differential Equations” (AMADE-2006), Minsk, Belarus, September 13-19, 2006

The Belarusian State University and the Institute of Mathematics of the Belarusian National Academy of Sciences together with Moscow State University organized the fourth International Conference "Analytic Methods of Analysis and Differential Equations" (ÀÌÀDÅ-2006) in September, 2006, in Minsk, Belarus. The Conference was dedicated to centenary of academician Fedor Dmitrievich Gakhov (1906-1980). It kept the tradition of previous conferences "Boundary Value Problems, Fractional Calculus and Special Functions" (1996) and "Analytic Methods of Analysis and Differential Equations" (1999, 2001, 2003), held in Minsk, Belarus.

The Conference was organized under the guidance of the International Society for Analysis, its Applications, and Computation (ISAAC) and was included in the calendar of the events of the European Mathematical Society.

Information on the Conference was published in the Journal “Fractional Calculus and Applied Analysis” and in the bulletin “Orthogonal Polynomial and Special Functions” of SIAM Activity Group on Orthogonal Polynomial and Special Functions.

396 mathematicians from Europe, Africa, America and Asia confirmed their interest in the Conference. 244 representatives of Algeria, Armenia, Belarus, Canada, France, Germany, Great Britain, Israel, Italy, Japan, Kazakhstan, Lithuania, Mexico, Poland, Portugal, Russia, Serbia, Slovenia, Ukraine and USA took part in AMADE-2006.

The main aspects presented at the conference were:

1. Boundary Value Problems for Analytic Functions.

2. Differential Equations and Applications.

3. Integral Transforms and Special Functions.

4. Integral and Integro-Differential Equations and Fractional Calculus.

5. Approximations and Operator Theory.

6. Applications to problems of mathematical physics and mechanics.

The conference was opened by the co-chairman of AMADE-2006, rector of Belarusian State University Professor V. I. Strazev. The plenary session was opened with a report on the life and scientific activity of academician F. D. Gakhov:
Kilbas A.A. (Minsk, Belarus): Fedor Dmitrievich Gakhov (the centenary of birthday).

There were 28 plenary invited lectures and 171 sectional talks devoted to different problems of classical and modern analysis, differential equations and their applications.

Plenary invited lectures were given by the following mathematicians:

Aksentiev L.A., Elizarov M.A. (Kazan, Russia) The role of F.D. Gakhov in the creation of the theory of inverse boundary value problems.

Alekhno A.G. (Minsk, Belarus) Homogeneous Riemann boundary value problem with real coefficients having infinite set of bounded solutions.

Begehr H. (Berlin, Germany) Polyharmonic functions and Dirichlet problems.

Burenkov V.I. (Cardiff, UK) General theorems on spectral stability of nonnegative self-adjoint operators.

Butzer P.L., Stens R.L. (Aachen, Germany) Prediction in terms of samples from the past: error estimates by a modulus covering discontinuous signals.

Glaeske H.-J. (Jena, Germany) On convolutions and orthogonal polynomials.

Izobov N.A., Mazanik S.A. (Minsk, Belarus) On asymptotic equivalence of linear differential systems under exponential perturbations.

Karlovich Yu.I. (Cuernavaca, Mexico) Pseudo-differential operators with nonregular symbols and their applications to the Riemann and Haseman boundary value problems.

Kilbas A.A. (Minsk, Belarus) Method of integral transforms in the theory of fractional differential equations.

Korzyuk V.I., Cheb E.S. (Minsk, Belarus) Generalized classical solution of boundary value problems for a hyperbolic equation of second order.

Lanza de Christoforis M. (Padova, Italy) Comparison of the eigenvalues of closed non-negative self-adjoint operators.

Laurincikas A. (Vilnius, Lithuania) The joint universality of periodic Hurwitz zeta-functions.

Mityushev V.V. (Krakov, Poland) Solution to the Riemann boundary value problem with piecewise constant matrix.

Nasyrov S.R. (Kazan, Russia) Development of F.D. Gakhov’s ideas in the topological theory of functions of the complex variable.

Obnosov Yu.V. (Kazan, Russia) Some generalizations of Milne-Thomson theorem.

Panov E.Yu. (Novgorod, Russia) Existence of strong traces for quasi-solutions of scalar conservative laws.

Prilepko A.I. (Moscow, Russia) Prediction-observation and non-local problems for evolution systems with distributed parameters.

Radkevich E.V., Palin V.V. (Moscow, Russia) On a behavior of solutions to systems of hyperbolic equations with relaxation on large instants.

Rogosin S.V. (Minsk, Belarus) Complex-analytic methods in applied sciences.

Rutkauskas S. (Vilnius, Lithuania) On the Dirichlet type problems to systems of degenerate elliptic equations.

Samko S.G. (Faro, Portugal) Classical operators of analysis - maximal, singular and potential - operators in variable exponent spaces.

Silvestrov V.V. (Moscow, Russia), Antipov Yu.A. (Louisiana, USA) Method of Riemann surfaces in fluid and solid mechanics.

Soldatov A.P. (Belgorod, Russia) On singular integral operators with a shift.

Sheshko M.A. (Lublin, Poland) On solution in closed form of a class of singular integral equations of the first kind with Cauchy kernel.

Shkalikov A.A. (Moscow, Russia) Spectral portraits of non self-adjoint Shturm-Liouville operators in the quasi-classical limit.

Vu Kim Tuan (Carrlolton, USA) Uncertainty principles for the Hankel transforms.

Wegert E., von Wolfersdorf L. (Freiberg, Germany) A solution method for the linear Chandrasekhar equation.

Yurchuk N.I. (Minsk, Belarus) A priori estimates and a continuous dependence of solutions of evolution equations on the changes of the boundary conditions.

During the conference a special session “Qualitative Theory of Partial Differential Equations” was organized by Profs M. Raisig (Germany), F. Hirosava (Japan) and E. V. Radkevich (Russia).

The proceedings of AMADE-2006 involving most of the section talks, were published in three volumes “Analytical Methods of Analysis and Differential Equations”, Vol. 1-3, Minsk, Institute of Mathematics, National Academy of Sciences of Belarus, 2006. The papers devoted to integral transforms and special functions will be included in a special issue of the Journal “Integral Transforms and Special Functions”.

The present volume contains some of the plenary lectures and section talks. The following aspects of the complex and functional analysis are included: boundary value problem for analytic and generalized analytic functions, integral operators and harmonic analysis. This volume includes such fields of ordinary and partial differential equations as difference matrix equations and systems, differential equations with fractional derivatives, hyperbolic, parabolic and operator-differential equations, differential equations on graphs. Applications to mechanics of composite materials and fluid mechanics are given.

At the final meeting the participants supported the suggestion to organize next AMADE-Conference in 2009.

The Organizing Committee is grateful to the Belarusian State University and the Belarusian Fundamental Research Fund and some other sponsors for their financial support.

© Amade 2009