Přednášky

Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

Spectral resolutions for non-self-adjoint convolution operators

Čtvrtek 20. června 2024 v 11:00

Abstract. This talk presents a spectral theory for a class of non-self-adjoint convolution type operators. Particular attention is paid to spectral decomposition (in terms of suitable invariant chains) of the convolution operators under consideration, summing up the extension to them of the classical Schur theory on the triangular decomposition of matrices. It is considered the general case of operators defined on Banach spaces. Applications to the spectral theory of periodic Jacobi type operators that are applicable to mathematics, physics, mathematical physics and others will also be given.

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese Dr. Ewelina Zalot,

Faculty of Applied Mathematics, AGH University of Krakow, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

Přednáška je určena všem zájemcům o problematiku.

Ing. Jan Holešovský, Ph.D.

vedoucí ÚMDG

Leták

Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

Conditional Lipschitz shadowing for ordinary differential equations

Úterý 29. srpna 2023 ve 13:00

Abstract. We introduce the notion of conditional Lipschitz shadowing which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain nonautonomous ordinary differential equations have such a property. The first criterion applies to a semilinear differential equation provided that its linear part is hyperbolic and the nonlinearity is small in a neighborhood of the prescribed set. The second criterion requires that the logarithmic norm of the derivative of the right-hand side with respect to the state variable is uniformly negative in a neighborhood of the prescribed set. The results are applicable to important classes of model equations including the logistic equation, whose conditional shadowing has recently been studied. Several examples are constructed showing that the obtained conditions are optimal.

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese prof. Mihály Pituka,

Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary

Přednáška je určena všem zájemcům o problematiku. Uskuteční za podpory programu Excelence RP902315002 a PPSŘ RP122314001.