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Katedra Analizy Nieliniowej i Statystyki


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Rok 2021
  • Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures


    Various equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....

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  • Smooth Orthogonal Projections on Riemannian Manifold


    We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....

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Rok 2020
Rok 2019
Rok 2018
Rok 2017
  • Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations

    In this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.

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  • Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
    • K. Szymański
    • B. Collins
    • T. Szarek
    • K. Życzkowski

    - Journal of Physics A-Mathematical and Theoretical - Rok 2017

    The convex set of quantum states of a composite K×K system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For K >3 or K=3 this algorithm works faster than sampling over the entire set of states and verifying whether the partial transpose is positive....

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  • E-cohomological Conley index

    - Rok 2017

    In this thesis we continue with developing the E-cohomological Conley index which was introduced by A.Abbondandolo. In particular, we generalize the index to non-gradient flows, we show that it an possesses additional multiplicative structure and we prove the continuation principle. Then, using continuation principle, we show how the computation of the E-cohomological Conley index can be reduced to the computation of the classical...

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  • Equations with Separated Variables on Time Scales

    We show that the well-known theory for classical ordinary differential equations with separated variables is not valid in case of equations on time scales. Namely, the uniqueness of solutions does not depend on the convergence of appropriate integrals.

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  • Grupa gdańskich topologów

    - Rok 2017

    Artykuł o charakterze przeglądowym. Jako rozdział 6 w książce zawiera przegląd najważniejszych rezultatów badawczych uzyskanych przez dużą grupę matematyków związanych z Uniwersytetem i Politechniką Gdańską określanych potocznie grupą topologów, a także uwagi historyczne dotyczące rozwoju tych zespołów. Dołączono i pokrótce omówiono obszerną bibliografię.

  • Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces

    In this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...

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  • On the existence of homoclinic type solutions of inhomogenous Lagrangian systems

    We study the existence of homoclinic type solutions for a class of inhomogenous Lagrangian systems with a potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and a square integrable forcing term. A homoclinic type solution is obtained as a limit of periodic solutions of an approximative sequence of second order differential equations.

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Rok 2016
Rok 2015
Rok 2014
Rok 2013