Title: Invariance property of minimal prime ideals

Abstract

Title: Generalized Hermite polynomials in the description of Chebyshev-like polynomials

Abstract: This presentation is a survey on the description of the main properties of the multi-index or multi-dimensional Chebyshev polynomials, by using the generalized Hermite polynomials as tool. The Hermite polynomials play a fundamental role in the extension of the classical special functions to the multidimensional or multi-index case. We will also show that, starting from the multi-index Hermite polynomials, it is possible to introduce the Chebyshev polynomials of multidimensional type of first and second kind, and some of their generalizations.

Title: Real interpolation methods with function parameter

Abstract: In the first part of my talk I will give a short introduction of the theory interpolation of linear operators. We give definitions of classical Lions-Peetre real interpolation methods (K and J methods), and some basic properties and theorems. In the second part of my talk I will discussed about two types of generalization of the classical Lions-Peetre real interpolation method using a function parameter. First was consider by Gustavsson [G] and second was con-sidered by Janson [J]. We will show the relation with these two methods. The original definition of Gustavsson was restricted on the so-call quasi-power parameter. We are able to consider this method for general function. Using the ideas from the book [EGO], we to show that the generalized method of Gustavsson and Janson's method are equivalent. Many properties which was obtained by Janson was problem to get for original Gustavsson method. It was reason that Gustavsson consider restricted class of parameter. We will obtained results for general Gustavson method without any restriction on the parameter.
References
[EGO] W.D. Evans, A. Gogatishvili, B. Opic, Weighted inequalities involving ρ- quasiconcave operators. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018.
[G] J. Gustavsson.A function parameter in connection with interpolation of Banach spaces. Math. Scand. 42 (1978), 289305.
[J] S. Janson. Minimal and maximal methods of interpolation, J. Funct. Anal., 44 (1981), 5073.

Title: Lie group techniques for differential equations

Abstract: Lie group analysis was created by the profound Norwegian mathematician Marius Sophus Lie (1842-1899) in the latter half of the nineteenth century. This technique systematically connects and broadens the well-known ad hoc methods to construct closed-form solutions of differential equations, particularly for nonlinear differential equations. In this talk we present Lie’s theory in brief and its applications to differential equations.

Title: Regularity properties for fractional Boussinesq equations and applications

Abstract: In this talk, the existence, uniqueness and regularity properties of solution of the Cauchy problem for the fractional abstract Boussinesq equation is ob- tained. First, we consider the linear Boussinesq equation and prove the ex- sistense, uniquness and the regularity properties of soluttions. It can be used to obtain the exsistense an uniquness of the regular solution of corresponding nonlinear Boussinesq equation. By applying this result, the Cauchy problem for finite or infinite systems of Boussinesq equations are studied.