I.A. Kipriyanov's Voronezh school on the theory of partial differential equations with singularities in coefficients. Transformation operators

Abstract: The main topic of the report is a communication on Voronezh School of I.A. Kiptiyanov on singular differential equations. Specially DE with Bessel operators are considered. Main results of Kipriyanov himself and his school are outlined: weighted functional spaces (Kipriyanov functional spaces), classification and research of differential equations with Bessel operators, spectral theory, B-hyperbolic equations (plane waves, fundamental solutions, formulas of Herglots-Petrovskii type, equations in Riemann spaces, problems and solutions with essential singularities and so on). Main instruments in these works are mentioned, such as transmutations, Fourier-Bessel transform, generalized translations. More detailed main works of two mathematicians are considered — of V.V. Katrakhov and V.Z. Meshkov. Modern papers in these fields are shortly outlined.

Russianmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods