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Infinite dimension of solutions of the Dirichlet problem

100%

Ryazanov V.

Open Mathematics

2015

tom 13

nr 1

It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

Affine Baire functions on Choquet simplices

88%

Kačena M., Spurný J.

Open Mathematics

2011

tom 9

nr 1

127-138

We construct a metrizable simplex X such that for each n ɛ ℕ there exists a bounded function f on ext X of Baire class n that cannot be extended to a strongly affine function of Baire class n. We show that such an example cannot be constructed via the space of harmonic functions.

Vector-valued holomorphic and harmonic functions

88%

Arendt W.

Concrete Operators

2016

tom 3

nr 1

68-76

Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.

Ograniczanie wyników

2 Open Mathematics

1 Concrete Operators

1 Arendt W.

1 Kačena M.

1 Ryazanov V.

1 Spurný J.

1 2016

1 2015

1 2011

Wyniki wyszukiwania

Infinite dimension of solutions of the Dirichlet problem

Affine Baire functions on Choquet simplices

Vector-valued holomorphic and harmonic functions