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1

Approximation by weighted polynomials in $ℝ^k$

100%

Branker M.

Annales Polonici Mathematici

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2005

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tom 85

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nr 3

261-279

EN

We apply pluripotential theory to establish results in $ℝ^k$ concerning uniform approximation by functions of the form wⁿPₙ where w denotes a continuous nonnegative function and Pₙ is a polynomial of degree at most n. Then we use our work to show that on the intersection of compact sections $Σ ⊂ ℝ^k$ a continuous function on Σ is uniformly approximable by θ-incomplete polynomials (for a fixed θ, 0 < θ < 1) iff f vanishes on θ²Σ. The class of sets Σ expressible as the intersection of compact sections includes the intersection of a symmetric convex compact set with a single orthant.

2

Lelong classes on toric manifolds and a theorem of Siciak

63%

Branker M., Stawiska M.

Annales Polonici Mathematici

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2012

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tom 106

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nr 1

97-105

EN

We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.

3

Weighted pluripotential theory on compact Kähler manifolds

63%

Branker M., Stawiska M.

Annales Polonici Mathematici

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2009

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tom 95

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nr 2

163-177

EN

We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Branker M.

2 Stawiska M.

1 2012

1 2009

1 2005

Approximation by weighted polynomials in $ℝ^k$

Lelong classes on toric manifolds and a theorem of Siciak

Weighted pluripotential theory on compact Kähler manifolds