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On some shift invariant integral operators, univariate case

George A. Anastassiou, Heinz H. Gonska (1995)

Annales Polonici Mathematici

In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and...

On spaces with the ideal convergence property

Jakub Jasinski, Ireneusz Recław (2008)

Colloquium Mathematicae

Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to I b , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.

On stability and the Łojasiewicz exponent at infinity of coercive polynomials

Tomáš Bajbar, Sönke Behrends (2019)

Kybernetika

In this article we analyze the relationship between the growth and stability properties of coercive polynomials. For coercive polynomials we introduce the degree of stable coercivity which measures how stable the coercivity is with respect to small perturbations by other polynomials. We link the degree of stable coercivity to the Łojasiewicz exponent at infinity and we show an explicit relation between them.

On stability of Alexander polynomials of knots and links (survey)

Mikami Hirasawa, Kunio Murasugi (2014)

Banach Center Publications

We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.

On stable polynomials

Miloslav Nekvinda (1989)

Aplikace matematiky

The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.

On subordination for classes of non-Bazilevič type

Rabha Ibrahim, Maslina Darus, Nikola Tuneski (2010)

Annales UMCS, Mathematica

We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.

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