Functional Analysis

This research group aims to advance our understanding of Lipschitz function spaces, Lipschitz-free spaces, and tensor products by developing and applying our existing knowledge of the extremal geometric structure of Banach spaces. Lipschitz functions are the most natural non-linear analog to continuous linear operators between Banach spaces. Every Lipschitz function between metric spaces admits a canonical linear extension between the corresponding Lipschitz-free spaces. Non-linear functional analysis is a comparatively new and active field of research with many unsolved internal problems, deep connections to related fields, and applications in discrete mathematics, optimal transport theory, graph theory, and computer science. Besides the scientific results, this project aims to produce PhDs for the needs of Estonia.

Research Group staff

Topics:

  • diameter two properties and their dual properties;
  • geometric structure of Lipschitz function spaces and Lipschitz-free spaces;
  • existence and characterizations of Daugavet- and Delta-points;
  • the uniqueness of extensions in the Hahn-Banach theorem;
  • ball-covering properties;
  • plasticity of the unit ball.

Research Group projects

Current projects

  • PRG877 Extremal geometric structure of Banach spaces with applications to the study of Lipschitz function spaces, Lipschitz free spaces, and tensor products
  • PSG487 The big slice phenomena in Banach spaces with applications to the study of Lipschitz spaces

Main past projects

  • MOBTP138 Diameter two properties in Lipschitz spaces and in tensor products of Banach spaces (08.2019-12.2019)
  • PUTJD702 Geometry of the unit ball of a Banach space and the connections to diameter two properties (08.2018-07.2019)
  • IUT20-57 Structural Problems in Analysis, Algebra, and Geometry, with Applications to Numerical Analysis (01.2014-12.2019)

Relevant publications

Recently defended doctoral dissertations

Seminar on Functional Analysis
The seminar covers topics of interest of the Functional Analysis Research Group of the University of Tartu about the geometry of Banach spaces. During the seminars, the members of the research group, including students, present their latest research results. Invited (foreign) guests of the seminar will also speak to give us an overview of their research topics, to introduce their main results and ideas, and to share the current problems that have arisen and their attempts to solve them.

#research #for society

Doctoral defence: Mohammed Mainul Hossain “Numerical analysis of vibrations of nanobeams”

Doctoral defence: Mohammed Mainul Hossain “Numerical analysis of vibrations of nanobeams”
21.07.2022
#research #for society

Doctoral defence: Andre Ostrak “Diameter two properties in spaces of Lipschitz functions”

Doctoral defence: Andre Ostrak "Diameter two properties in spaces of Lipschitz functions“
21.07.2022
#research #for society

Doctoral defence: Kristo Väljako "On the Morita equivalence of idempotent rings and monomorphisms of firm bimodules“

Doctoral defence: Kristo Väljako "On the Morita equivalence of idempotent rings and monomorphisms of firm bimodules“
21.07.2022