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Rational interpolants with preassigned poles, theoretical aspects

100%

Ambroladze A., Wallin H.

Studia Mathematica

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1999

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tom 132

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nr 1

1-14

EN

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 ${b_{ni}}^{n}_{i=1}$ and interpolating ⨍ at the points ${a_{ni}}^{n}_{i=0}$. 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 ${b_{ni}}_{i,n}$ without limit points on K. In this paper we study the case of general compact sets K, when such a separation is not always possible. This fact causes changes both in the results and in the methods of proofs. We consider also the case of functions analytic in open domains. It turns out that in our general setting there is no longer a "duality" ([8], Section 8.3, Corollary 2) between the poles and the interpolation points.

2

The dual of Besov spaces on fractals

100%

Jonsson A., Wallin H.

Studia Mathematica

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1994-1995

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tom 112

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nr 3

285-300

EN

For certain classes of fractal subsets F of $ℝ^n$, the Besov spaces $B_α^{p,q}(F)$ have been studied for α > 0 and 1 ≤ p,q ≤ ∞. In this paper the Besov spaces $B_α^{p,q}(F)$ are introduced for α < 0, and it is shown that the dual of $B_α^{p,q}(F)$ is $B_{-α}^{p',q'}(F), α ≠ 0, 1 < p,q < ∞, where 1/p + 1/p' = 1, 1/q + 1/q' = 1.

3

Hardy and Lipschitz spaces on subsets of $R^{n}$

60%

Jonsson A., Sjögren P., Wallin H.

Studia Mathematica

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1984

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tom 80

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nr 2

141-166

Ograniczanie wyników

3 Studia Mathematica

3 Wallin H.

2 Jonsson A.

1 Ambroladze A.

1 Sjögren P.

1 1999

1 1995

1 1984

Rational interpolants with preassigned poles, theoretical aspects

The dual of Besov spaces on fractals

Hardy and Lipschitz spaces on subsets of $R^{n}$