Displaying similar documents to “Algebras of generalized analytic functions”

Equivalence of analytic and rational functions

J. Bochnak, M. Buchner, W. Kucharz (1997)

Annales Polonici Mathematici

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We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.

A new rational and continuous solution for Hilbert's 17th problem.

Charles N. Delzell, Laureano González-Vega, Henri Lombardi (1992)

Extracta Mathematicae

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In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is...

Rational interpolants with preassigned poles, theoretical aspects

Amiran Ambroladze, Hans Wallin (1999)

Studia Mathematica

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Let ⨍ be an analytic function on a compact subset K of the complex plane ℂ, and let r n ( z ) denote the rational function of degree n with poles at the points b n i i = 1 n and interpolating ⨍ at the points a n i i = 0 n . We investigate how these points should be chosen to guarantee the convergence of r n to ⨍ as n → ∞ for all functions ⨍ analytic on K. When K has no “holes” (see [8] and [3]), it is possible to choose the poles b n i i , n without limit points on K. In this paper we study the case of general compact sets K, when...