This book features papers presented during a special session on algebra, functional analysis, complex analysis, and pluripotential theory. Research articles focus on topics such as slow convergence, spectral expansion, holomorphic extension, m-subharmonic functions, pseudo-Galilean group, involutive algebra, Log-integrable measurable functions, Gibbs measures, harmonic and analytic functions, local automorphisms, Lie algebras, and Leibniz algebras. Many of the papers address the theory of harmonic functions, and the book includes a number of extensive survey papers. Graduate and researchers interested in functional analysis, complex analysis, operator algebras and non-associative algebras will find this book relevant to their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference's scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Differential Equations and Dynamical Systems is also published in the Springer Proceedings in Mathematics & Statistics Series.

Features surveys related to the topics covered Includes open problems for future investigation Presents recent results on algebra, functional analysis, complex analysis, and pluripotential theory

Inhalt
Abdullaev, B. I., Imomkulov, S. A. and Sharipov, R.A: Removable Singular Sets of Msubharmonic Functions.- Aksoy, A. G: Extensions of Bernstein's Lethargy Theorem.- Ayupov, Sh. A. and Kudaybergenov, K: Local Automorphisms on Finite-dimensional Lie and Leibniz Algebras.- Babajanov, B. A: Integration of the Toda-type Chain with a Special Self-consistent Source.- Botirov, G. I. and Rahmatullaev, M. M: Ground States for Potts Model with a Countable Set of Spin Values on a Cayley tree.- Abdullaev, R. Z. and Chilin, V. I: Isomorphic Classication of -Algebras of Log-integrable Measurable Functions.- Chilin, V. I. and Muminov, K. K: Matrix Dierential Equations for Pseudo-orthogonal Groups.- Kadyrov, S. and Sapazhanov, Y: Polynomial Estimates over Exponential Curves in C2.- Khudayberganov, G. and Rakhmonov, U. S: Carleman Formula for Matrix Ball of the Third Yype.- Otemuratov, B: A Multidimensional Boundary Analogue of Hartogs Theorem on ncircular Domains for Integrable Functions.- Prenov, B. B: On the Number of Real Zeros of Entire Functions of Finite Order of Growth.- Rakhimov, I. S: On Extensions of Some Classes of Algebras.- Rozikov, U. A: Holliday Junctions for the Potts Model of DNA.- Sadullaev, A: Further Developments of the Pluripotential Theory (survey).- Sadullaeva, Sh. A. and Khojimurodova, M. B: Properties of Solutions of the Cauchy Problem for Degenerate Nonlinear Cross Systems with Convective Transfer and Absorption.- Sadullaev, A. and Ibragimov, Z: Class R of Gonchar in Cn.- Dukenbayeva, A. A., Sadybekov, M. A. and Yessirkegenov. N. A: On a Generalised SamarskiiIonkin Type Problem for the Poisson Equation.- Sattarov, I. A: Ergodicity Properties of p-adic (2; 1)-rational Dynamical Systems with Unique Fixed Point.