| 1. |
- Andersson, Johan, 1971-, et al.
(författare)
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Mergelyan’s theorem with polynomials non-vanishing on unions of sets
- 2014
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Ingår i: Complex Variables and Elliptic Equations. - : Taylor & Francis. - 1747-6933 .- 1747-6941. ; 59:1, s. 99-109
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of approximating a function having no zeros on the interior of a set by polynomials having no zeros on the entire set.
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| 2. |
- Andersson, Mats, 1957
(författare)
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Pseudomeromorphic currents on subvarieties
- 2016
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941. ; 61:11, s. 1533-1540
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Tidskriftsartikel (refereegranskat)abstract
- Let i : X --> Y be pure-dimensional reduced subvariety of a smooth manifold Y. We prove that direct images of pseudomeromorphic currents on X are pseudomeromorphic on Y. We also prove a partial converse: if i(*)tau is pseudomeromorphic and has the standard extension property, then tau is pseudomermorphic on X.
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| 3. |
- Avelin, Benny, et al.
(författare)
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Approximation of plurisubharmonic functions
- 2016
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941. ; 61:1, s. 23-28
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Tidskriftsartikel (refereegranskat)abstract
- We extend a result by Fornaaess and Wiegerinck [Ark. Mat. 1989;27:257-272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.
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| 4. |
- Beilina, Larisa, 1970, et al.
(författare)
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The philosophy of the approximate global convergence for multidimensional coefficient inverse problems
- 2012
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941. ; 57:2-4, s. 277-299
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Tidskriftsartikel (refereegranskat)abstract
- Both the most important and the most challenging question in the numericaltreatment of a Multidimensional Coefficient Inverse Problem for a PDE is thefollowing: How to obtain a point in a small neighborhood of the exactsolution without any a priori knowledge of this solution? The recentnumerical experience of the authors for two types of MultidimensionalCoefficient Inverse Problems shows that in order to develop a trulyefficient algorithm addressing this question, it is necessary to make somereasonable approximations which cannot be rigorously justified.Nevertheless, numerical studies show that corresponding algorithms workquite well. The authors call this approach "approximateglobal convergence/reconstruction". The goal of the paper is to present ashort illustrative review of this philosophy.
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| 5. |
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| 6. |
- Björn, Anders
(författare)
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Removable singularities for hardy spaces
- 1998
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941. ; 35:1, s. 1-25
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study removable singularities for Hardy spaces of analytic funtions on general domains. Two different definitions are given. For compact sets they turn out to be equal and moreover independent of the surrounding domain, as was proved by D. A Hejhal For non-compact sets the difference between the definitions is studied. A survey of the present knowledge is given, except for the special cases of singularities lying on curves and singularities being self-similar Cantor sets, which the author deals with in other papers. Among the results is the non-removability for Hp of sets with dimension greater than ρ. 0 < ρ < 1. Many counterexamples are provided and the Hp capacities are introduced and studied.
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| 7. |
- Björn, Anders
(författare)
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The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications
- 2019
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Ingår i: Complex Variables and Elliptic Equations. - : TAYLOR & FRANCIS LTD. - 1747-6933 .- 1747-6941. ; 64:1, s. 40-63
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is obtained for a large class of compactifications, but also two examples when it fails are given. This study is done for complete metric spaces equipped with doubling measures supporting a p-Poincare inequality, but the results are new also in unweighted Euclidean spaces.
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| 8. |
- Carlsson, Linus, 1972-, et al.
(författare)
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A note on B-envelope of holomorphy and B-extendable domains
- 2008
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Ingår i: Complex Variables and Elliptic Equations. - Abingdon, Oxon, UK : Taylor & Francis. - 1747-6933 .- 1747-6941. ; 53:4, s. 307-309
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Tidskriftsartikel (refereegranskat)abstract
- Let B subset of H(infinity)(X) be a Banach Algebra on a Riemann domain X over C(n). We show that under certain conditions on B and X, all functions in B can be extended to functions in B(E(B, X)) where E(B, X) is the B-envelope of holomorphy.
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| 9. |
- Cialdea, A., et al.
(författare)
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The L-p-dissipativity of first order partial differential operators
- 2018
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Ingår i: Complex Variables and Elliptic Equations. - : TAYLOR & FRANCIS LTD. - 1747-6933 .- 1747-6941. ; 63:7-8, s. 945-960
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Tidskriftsartikel (refereegranskat)abstract
- We find necessary and sufficient conditions for the L-p-dissipatiyity of the Dirichlet problem for systems of partial differential operators of the first order with complex locally integrable coefficients. As a by product we obtain sufficient conditions for a certain class of systems of the second order.
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| 10. |
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