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pro vyhledávání: '"Samuelsson, Håkan"'
Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and $F$ we sho
Externí odkaz:
http://arxiv.org/abs/1101.4840
Autor:
Andersson, Mats, Samuelsson, Håkan
Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\dbar$-equation. We obtain new existence results for the $\dbar$-equation, as well as new
Externí odkaz:
http://arxiv.org/abs/1012.4269
Autor:
Andersson, Mats, Samuelsson, Håkan
Let $X$ be a complex space of pure dimension. We introduce fine sheaves $\A^X_q$ of $(0,q)$-currents, which coincides with the sheaves of smooth forms on the regular part of $X$, so that the associated Dolbeault complex yields a resolution of the str
Externí odkaz:
http://arxiv.org/abs/1010.6142
Autor:
Lärkäng, Richard, Samuelsson, Håkan
Publikováno v:
J. Funct. Anal. 264 (2013), no. 1, 118-138
We describe various approaches to Coleff-Herrera products of residue currents $R^j$ (of Cauchy-Fantappi\`e-Leray type) associated to holomorphic mappings $f_j$. More precisely, we study to which extent (exterior) products of natural regularizations o
Externí odkaz:
http://arxiv.org/abs/1005.2056
Autor:
Samuelsson, Håkan, Seppänen, Henrik
We construct Koppelman formulas on manifolds of flags in $\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theo
Externí odkaz:
http://arxiv.org/abs/1003.5646
Autor:
Björk, Jan-Erik, Samuelsson, Håkan
Publikováno v:
J. reine angew. Math., 649 (2010)
Under assumptions about complete intersection, we prove that Coleff-Herrera type currents satisfy a robust calculus in the sense that natural regularizations of such currents can be multiplied to yield regularizations of the Coleff-Herrera product of
Externí odkaz:
http://arxiv.org/abs/0811.2158
Publikováno v:
Ann. Inst. Fourier, Tome 60, no 2 (2010)
Let $Z$ be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briancon-Skoda theorem for the local ring $\mathcal{O}_Z$; a result which was previously proved by Huneke by algebraic methods. For ideals wi
Externí odkaz:
http://arxiv.org/abs/0806.3700
Autor:
Andersson, Mats, Samuelsson, Håkan
Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\dbar$-equation. We prove that if $\phi$ is a smooth $(0,q+1)$-form on a Stein space $X$
Externí odkaz:
http://arxiv.org/abs/0801.0710
Autor:
Samuelsson, Håkan
Let $X$ be a complex manifold and $f\colon X\to \C^p$ a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated to $f$ has an analytic continuation to a neighborhood of the
Externí odkaz:
http://arxiv.org/abs/0709.1597
We construct Koppelman formulas on Grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual. As a consequence we obtain some vanishing theorems of the Bott-Borel-Weil type. We also r
Externí odkaz:
http://arxiv.org/abs/0709.1559