Integral representation with weights. I

DOI10.1007/s00208-003-0382-4zbMath1024.32005OpenAlexW2014396503MaRDI QIDQ1396483

Mats Andersson

Publication date: 2 July 2003

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-003-0382-4

zbMATH Keywords

strictly pseudoconvex domainsDolbeault isomorphismanalytic polyhedronCauchy-Fantappie-Leray formulaCauchy-Weil formuladivision and interpolation formulasKoppelman formulas for \(\overline\partial\)representation formulas for holomorphic functionsweighted representation formulas

Mathematics Subject Classification ID

Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (29)

The membership problem for polynomial ideals in terms of residue currents ⋮ Ideals of smooth functions and residue currents ⋮ Integral representation with weights. II: Division and interpolation ⋮ Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags ⋮ Division formulas on projective varieties ⋮ Explicit Serre duality on complex spaces ⋮ The \(\bar{\partial}\)-equation, duality, and holomorphic forms on a reduced complex space ⋮ Explicit versions of the Briançon-Skoda theorem with variations ⋮ Boundary behavior of functions representable by weighted Koppelman type integral and related Hartogs phenomenon ⋮ A residue calculus approach to the uniform Artin-Rees lemma ⋮ Koppelman formulas on flag manifolds and harmonic forms ⋮ A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas ⋮ (Ultra)differentiable functional calculus and current extension of the resolvent mapping. ⋮ Explicit representation of membership in polynomial ideals ⋮ Norm estimates for the \(\bar{\partial}\)-equation on a non-reduced space ⋮ Some variants of Macaulay's and Max Noether's theorems ⋮ The flatness of the \(\mathcal{O}\)-module of smooth functions and integral representation ⋮ An elementary proof of the Briançon-Skoda theorem ⋮ Integral formulas and the Ohsawa-Takegoshi extension theorem ⋮ Koppelman formulas on Grassmannians ⋮ Products of residue currents of Cauchy-Fantappiè-Leray type ⋮ Weighted integral formulas on manifolds ⋮ Regularity of pseudomeromorphic currents ⋮ Weighted Koppelman formulas and the \(\bar\partial\)-equation on an analytic space ⋮ Residue currents and ideals of holomorphic functions ⋮ On the Briançon-Skoda theorem on a singular variety ⋮ Integral representation of moderate cohomology ⋮ Global Koppelman formulas on (singular) projective varieties ⋮ Koppelman formulas on smooth compact toric varieties

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