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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 5, Pages 203–224 (Mi izv49)  

This article is cited in 4 scientific papers (total in 4 papers)

On the structure of residue currents and functionals orthogonal to ideals in the space of holomorphic functions

V. M. Trutnev, A. K. Tsikh

Krasnoyarsk State University

Abstract: This article investigates residues associated with holomorphic mappings $f=(f_1,…,f_p)\colon X\to\mathbb C^p$ defined on a complex space $X$. By means of a new definition of principal value of a residue, it sharpens results of Coleff, Herrera, and Dolbeault concerning the structure of residues. It establishes a connection between residues and functionals in $\mathcal O'(X)$ orthogonal to the ideal $\langle f_1,…,f_p\rangle\subset\mathcal O(X)$. Using these results on residues and functionals, a formula is derived for the exponential representation for elements of invariant subspaces and for the solution of homogeneous convolution equations.

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English version:
Izvestiya: Mathematics, 1995, 59:5, 1083–1102

Bibliographic databases:

MSC: 32C30, 32A27
Received: 24.01.1995

Citation: V. M. Trutnev, A. K. Tsikh, “On the structure of residue currents and functionals orthogonal to ideals in the space of holomorphic functions”, Izv. RAN. Ser. Mat., 59:5 (1995), 203–224; Izv. Math., 59:5 (1995), 1083–1102

Citation in format AMSBIB
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\by V.~M.~Trutnev, A.~K.~Tsikh
\paper On the structure of residue currents and functionals orthogonal to ideals in the space of holomorphic functions
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 5
\pages 203--224
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1360642}
\zmath{https://zbmath.org/?q=an:0876.32004}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 5
\pages 1083--1102
\crossref{https://doi.org/10.1070/IM1995v059n05ABEH000049}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alexandr G. Aleksandrov, Avgust K. Tsikh, “Multi-Logarithmic Differential Forms on Complete Intersections”, Zhurn. SFU. Ser. Matem. i fiz., 1:2 (2008), 105–124  mathnet  elib
    2. E. K. Leinartas, M. Passare, A. K. Tsikh, “Multidimensional versions of Poincaré's theorem for difference equations”, Sb. Math., 199:10 (2008), 1505–1521  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Pavel V. Trishin, “O meromorfnykh resheniyakh dvumernykh raznostnykh uravnenii”, Zhurn. SFU. Ser. Matem. i fiz., 2:3 (2009), 360–369  mathnet  elib
    4. Natalia A. Bushueva, Konstantin V. Kuzvesov, Avgust K. Tsikh, “On the asymptotic of homological solutions to linear multidimensional difference equations”, Zhurn. SFU. Ser. Matem. i fiz., 7:4 (2014), 417–430  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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