2023/2024

Топологические векторные пространства

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Когда читается: 1, 2 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Пирковский Алексей Юльевич

Язык: английский

Кредиты: 3

Контактные часы: 30

Course Syllabus

Abstract

"The traditional functional analysis deals mostly with Banach spaces and, in particular, Hilbert spaces. However, many classical vector spaces have canonical topologies that cannot be determined by a single norm. For example, many spaces of smooth functions, holomorphic functions, and distributions belong to the above class. Such spaces are the subject of the theory of topological vector spaces. Although the golden age of topological vector spaces was in the 1950ies, their theory is still evolving nowadays, contrary to a stereotyped view coming from incompetent sources. The current development of topological vector spaces is directed not so much towards general theory as towards applications in PDEs and in complex analytic geometry. We plan to discuss the basics of the theory of topological vector spaces (with an emphasis on tensor products and nuclear spaces), including some applications to distributions (the Schwartz Kernel Theorem) and/or complex analytic geometry (the Cartan-Serre Finiteness Theorem). "