Karlstad Applied Analysis Seminar (KAAS)

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Future seminars:

Talk-151

When: 15 Oct 2025, 10:30-11:15
What: On quasi-isometric liftings for operators on Hilbert spaces
Who: Andra-Maria Stoica, Lucian Blaga University of Sibiu, Romania.
Where: https://kau-se.zoom.us/j/61616693592

This presentation investigates quasi-isometric liftings for operators on Hilbert spaces that are similar to contractions. A bounded linear operator $T$ is said to be a quasi-isometry if it acts as an isometry on its range. The case of operators that are contractive on their range is also explored, providing a clear illustration of how the developed theory parallels the classical contraction setting. Special attention is given to liftings that are left-invertible and also liftings that resemble the classical Nagy–Foiaș isometric liftings for contractions.

The analysis highlights the role of wandering subspaces, as well as the Cauchy dual operator, in the study of left-invertible operators. These operators are significant due to their special actions and their connection with model theory, as they can be transformed into multiplication operators on model spaces such as classical function spaces including Lebesgue, Hardy, and Dirichlet spaces. As a consequence, the operators that admit such liftings can be also seen on model spaces and so they can be used in order to prove general interpolation problems for analytic functions.

Talk-152

When: T.B.D
What: Nonsmooth mechanics of fiber network microstructures
Who: Mykola Tkachuk, Karlstad University, Karlstad, Sweden.
Where: T.B.D and online: https://kau-se.zoom.us/j/61616693592
Abstract:

We wish to present the case that many problems in mechanics can be posed as mathematical programming.

Equilibrium of various structures can be determined via minimization of the potential energy or other suitable mechanical functional. We have developed a new discrete network model [2] for nonwoven materials.

The rate-independent sliding and the quasi-static equilibrium loading of such network structure are constituted within the theory of standard dissipative systems. A minimum principle for incremental potential is formulated with respect to the displacement-based variables: nodal coordinates, segment end-to-end vectors, segment lengths and incremental fiber slidings. It takes the form of second-order cone programming (SOCP) similarly to the case of elastic cable networks. A pure complementary energy principle is derived as the dual formulation in terms of stress-like variables: nodal reactions, fiber force vectors, axial forces and friction forces.

The model capture large irreversible deformations of nonwoven materials. The damage mechanism is implemented in the form of fiber pull-out. The network becomes disjoint as more and more sections of free tails are pulled through the end knots.