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Displaying 41 – 60 of 143

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The gradient lemma

Urban Cegrell (2007)

Annales Polonici Mathematici

We show that if a decreasing sequence of subharmonic functions converges to a function in W l o c 1 , 2 then the convergence is in W l o c 1 , 2 .

The homogeneous transfinite diameter of a compact subset of N

Mieczysław Jędrzejowski (1991)

Annales Polonici Mathematici

Let K be a compact subset of 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 N is computed.

The image of a finely holomorphic map is pluripolar

Armen Edigarian, Said El Marzguioui, Jan Wiegerinck (2010)

Annales Polonici Mathematici

We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.

The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces

Roman Lávička (1998)

Commentationes Mathematicae Universitatis Carolinae

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

Currently displaying 41 – 60 of 143