Wyniki wyszukiwania

1

On bivariate Hermite interpolation and the limit of certain bivariate Lagrange projectors

100%

Manh P.

Annales Polonici Mathematici

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2015

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tom 115

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nr 1

1-21

EN

We give a new poised bivariate Hermite scheme and a formula for the interpolation polynomial. We show that the Hermite interpolation polynomial is the limit of bivariate Lagrange interpolation polynomials at Bos configurations on circles.

2

Complete pluripolar graphs in $ℂ^N$

63%

Dieu N., Manh P.

Annales Polonici Mathematici

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2014

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tom 112

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nr 1

85-100

EN

Let F be the Cartesian product of N closed sets in ℂ. We prove that there exists a function g which is continuous on F and holomorphic on the interior of F such that $Γ_g(F):={(z, g(z)): z ∈ F}$ is complete pluripolar in $ℂ^{N+1}$. Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that $Γ_g(D)$ is complete pluripolar in $ℂ^{N+1}$. These results are high-dimensional analogs of the previous ones due to Edlund [Complete pluripolar curves and graphs, Ann. Polon. Math. 84 (2004), 75-86] and Levenberg, Martin and Poletsky [Analytic disks and pluripolar sets, Indiana Univ. Math. J. 41 (1992), 515-532].

3

A Determinantal Proof of the Product Formula for the Multivariate Transfinite Diameter

63%

Calvi J.-P., Manh P.

Bulletin of the Polish Academy of Sciences. Mathematics

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2005

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tom 53

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nr 3

291-298

EN

We give an elementary proof of the product formula for the multivariate transfinite diameter using multivariate Leja sequences and an identity on vandermondians.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Bulletin of the Polish Academy of Sciences. Mathematics

3 Manh P.

1 Calvi J.-P.

1 Dieu N.

1 2015

1 2014

1 2005

On bivariate Hermite interpolation and the limit of certain bivariate Lagrange projectors

Complete pluripolar graphs in $ℂ^N$

A Determinantal Proof of the Product Formula for the Multivariate Transfinite Diameter