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Currently displaying 1 – 5 of 5

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On the graph of a quasi-additive function.

M. Baran — 1990

Aequationes mathematicae

On two new functional equations for generalized Joukowski transformations

M. Baran; H. Haruki — 1991

Annales Polonici Mathematici

The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function $1 / 2 (z + z^{- 1})$ of a complex variable z.

Polynomial inequalities on algebraic sets

M. Baran; W. Pleśniak — 2000

Studia Mathematica

We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in $ℂ^{n}$ (resp. $ℝ^{n}$ ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.

Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves

M. Baran; W. Pleśniak — 1997

Studia Mathematica

We show that in the class of compact, piecewise $C^{1}$ curves K in $ℝ^{n}$ , the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.

Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities

M. Baran; W. Pleśniak — 2000

Studia Mathematica

We show that in the class of compact sets K in $ℝ^{n}$ with an analytic parametrization of order m, the sets with Zariski dimension m are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for tangential derivatives of (the traces of) polynomials on K.

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