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報告題目：Functional Calculus for Matrices and Operators

報告時間：2024年3月28日（星期四）15:10-17:00

報告地點：理學院B315

主辦單位：理學院

報告人：Maria Oreshina

報告人簡介：

Maria Oreshina received the degree in Applied Mathematics in 2001 in Lipetsk State Technical University (diploma with honor). In 2005,she made her promotion as a Candidate of Physical and Mathematical Sciences with the thesis “Operator Methods for the Investigation of Systems of Linear Differential Equations of Large Dimension”. Her scientific fields of interest are connected with approximate methods for differential equations and mathematical modeling of dynamic systems, technological processes and social/economic systems. Currently she specializes in Spectral Theory of Linear Operators and Functional Calculus for Operators.

報告內容簡介：

Functions of linear operators are considered. The cases of bounded and unbounded operators and operator pencils are discussed. The main applications are linear differential equations with self-adjoint operator coefficients, such as systems with matrices of large dimensions, parabolic equations and some others. The approximate method for such equations is suggested. A priori estimates of the approximation error are obtained. The results of numerical experiments are presented.

Special case is analytic functional calculus for two operators, acting in a Banach space. Properties and some applications are discussed.