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References [1] Anokhin , A. V. Berezansky , L. Braverman , E. 1995 Exponential stability of linear

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A necessary and sufficient criterion weaker than the Markoff's hypothesis for asymptotical stability of stochastic semigroups of Markov operators on (L)-spaces is proven.

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. Math. Comp. 2005 162 1485 1497 Yang, X. , On the global asymptotic stability

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. and Böröczky, K. J. Stability of some versions of the Prékopa-Leindler inequality, Monatshefte Math. , 163 (2011), 1–14. MR 2012b :52015 Böröczky K. J. Stability of some

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For a domain D, a pointpand a function f the integral M f (D; p)= Z D f(px)dx is called the moment of D with respect to p taken with the function f. Herepx denotes the distance of x to p. The Moment Theorem of László Fejes Tóth states the following: Let H be a convex polygon in E 2 with at most six sides and f a non-increasing function defined for non-negative reals. Let p1;pn be distinct points and let Di be the Dirichlet cell of pi relative to H. Then we have n P i=1 M f (Di; pi) 5 nM f (Hn; o); where Hn is a regular hexagon of area a(Hn)=a(H)=n centered at o. In the paper a stability criterion to the Moment Theorem is established.

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Abstract  

We prove a stability result for a family of functional equations containing the exponential and the Gołąb-Schinzel functional equations. Thus we extend and improve a recent result of J. Chudziak.

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Abstract  

We show that, in the classes of functions with values in a real or complex Banach space, the problem of Hyers-Ulam stability of a linear functional equation of higher order (with constant coefficients) can be reduced to the problem of stability of a first order linear functional equation. As a consequence we prove that (under some weak additional assumptions) the linear equation of higher order, with constant coefficients, is stable in the case where its characteristic equation has no complex roots of module one. We also derive some results concerning solutions of the equation.

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Abstract  

Uniform stability and localization results for the higher order and singular Kobayashi metrics are established. As an application we obtain the non-tangential weighted limits of these metrics in an h-extendible boundary point of a bounded domain in C n.

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Summary  

We study the stability of Gabor frames with arbitrary sampling points in the time-frequency plane, in several aspects. We prove that a Gabor frame generated by a window function in the Segal algebra S 0(R d) remains a frame even if (possibly) all the sampling points undergo an arbitrary perturbation, as long as this is uniformly small. We give explicit stability bounds when the window function is nice enough, showing that the allowed perturbation depends only on the lower frame bound of the original family and some qualitative parameters of the window under consideration. For the perturbation of window functions we show that a Gabor frame generated by any window function with arbitrary sampling points remains a frame when the window function has a small perturbation in S 0(R d) sense. We also study the stability of dual frames, which is useful in practice but has not found much attention in the literature. We give some general results on this topic and explain consequences to Gabor frames.

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Abstract  

We discuss the probabilistic stability of the equation µ ∘ fη = f, by using the fixed point method.

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