Pick-Nevanlinna interpolation on finitely-connected domains

Stephen Fisher

Displaying similar documents to “Pick-Nevanlinna interpolation on finitely-connected domains”

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...

A quadratic integral equation

Roger D. Nussbaum (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Blaschke products for finite Riemann surfaces

Balmohan Limaye (1970)

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A sum involving the function of Möbius

D. Lehmer, S Selberg (1960)

Acta Arithmetica

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Approximation on the sphere by Besov analytic functions

Evgueni Doubtsov (1997)

Studia Mathematica

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Boundary values of zero-smooth Besov analytic functions in the unit ball of $ℂ^{n}$ are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.

A kernel associated with certain multiply connected domains and its applications to factorization theorems

R. Coifman, Guido Weiss (1966)

Studia Mathematica

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Analytic continuation of fundamental solutions to differential equations with constant coefficients

Christer O. Kiselman (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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If $P$ is a polynomial in $R^{n}$ such that $1 / P$ integrable, then the inverse Fourier transform of $1 / P$ is a fundamental solution $E_{P}$ to the differential operator $P (D)$ . The purpose of the article is to study the dependence of this fundamental solution on the polynomial $P$ . For $n = 1$ it is shown that $E_{P}$ can be analytically continued to a Riemann space over the set of all polynomials of the same degree as $P$ . The singularities of this extension are studied.

On absolutely representing systems in spaces of infinitely differentiable functions

Yu. Korobeĭnik (2000)

Studia Mathematica

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The main part of the paper is devoted to the problem of the existence of absolutely representing systems of exponentials with imaginary exponents in the spaces $C^{\infty} (G)$ and $C^{\infty} (K)$ of infinitely differentiable functions where G is an arbitrary domain in $ℝ^{p}$ , p≥1, while K is a compact set in $ℝ^{p}$ with non-void interior K̇ such that $\bar{K} ̇ = K$ . Moreover, absolutely representing systems of exponents in the space H(G) of functions analytic in an arbitrary domain $G \subseteq ℂ^{p}$ are also investigated.