Abstract Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by Uvarov modification of given are studied. Existence is analyzed, stating conditions ensure it. The matrices the three explicitly terms satisfied original family. Two examples presented order show that results valid positive definite functionals and also some quasi w...

We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family Xε of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on Xε approximate those of the Laplacian with “free” boundary conditions on X0, the ...

It is a well-known fact that stable semantics might not provide any extensions for some given abstract argumentation framework. Arguably such frameworks might be considered futile, at least with respect to stable semantics. We propagate σ -perfection stating that for a given argumentation graph all induced subgraphs provide σ -extensions. We discuss perfection and conditions for popular abstrac...

How complex could the solution be to an initial value problem given by a polynomial-time computable function? This question can be given a natural and precise sense in computational complexity theory. In this note, we put together several results stating that more conditions on the problem make the solution simpler. In particular, Lipschitz continuity alone may leave the solution polynomial-spa...