Year 2022

• On a comparison principle and the uniqueness of spectral flow

  Publication

  • M. Starostka
  • N. Waterstraat

  - MATHEMATISCHE NACHRICHTEN - Year 2022

  The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply...

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Year 2004

• Existence of unbounded solutions to parabolic equations with functional dependence

  Publication

  • A. Bartłomiejczyk (formerly: A. Bychowska)

  - MATHEMATISCHE NACHRICHTEN - Year 2004

  The Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).

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Year 2002

• The asymptotic formula for the error in orthogonal projection

  Publication

  • M. Beśka
  • K. Dziedziul

  - MATHEMATISCHE NACHRICHTEN - Year 2002

  W pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.