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Alexander's projective capacity for polydisks and ellipsoids in $ℂ^N$

100%

Jędrzejowski M.

Annales Polonici Mathematici

1995

tom 62

nr 3

245-264

Alexander's projective capacity for the polydisk and the ellipsoid in $ℂ^N$ is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in $ℂ^N$ are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in $ℂ^N$ is proved to have an asymptotic behaviour in $ℂ^N$ similar to that of the Siciak homogeneous extremal function associated with K.

The homogeneous transfinite diameter of a compact subset of $ℂ^N$

100%

Jędrzejowski M.

Annales Polonici Mathematici

1991

tom 55

nr 1

191-205

Let K be a compact subset of $ℂ^N$. A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of $ℂ^N$ is computed.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Jędrzejowski M.

1 1995

1 1991

Wyniki wyszukiwania

Alexander's projective capacity for polydisks and ellipsoids in $ℂ^N$

The homogeneous transfinite diameter of a compact subset of $ℂ^N$