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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 566–597 (Mi izv1501)  

This article is cited in 7 scientific papers (total in 8 papers)

Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the Radon–Penrose transform

P. L. Polyakov, G. M. Henkin


Abstract: Global integral representations are constructed for differential forms on domains in complex projective space $\mathbf CP^n$.
Consequences of these representations are the following: first, criteria for the solvability of the inhomogeneous Cauchy–Riemann equations on $q$-pseudoconvex and $q$-pseudoconcave domains in an algebraic manifold; second, explicit formulas and bounds for solutions of these equations; and third, a description of the kernel and image and an inversion formula for the Radon-Penrose transform of $(0,q)$-forms on $q$-linearly concave domains in $\mathbf CP^n$.
Bibliography: 23 titles.

Full text: PDF file (3107 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 555–587

Bibliographic databases:

UDC: 517.55+539.12
MSC: Primary 32A25; Secondary 35N15, 32F20
Received: 16.03.1984

Citation: P. L. Polyakov, G. M. Henkin, “Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the Radon–Penrose transform”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 566–597; Math. USSR-Izv., 28:3 (1987), 555–587

Citation in format AMSBIB
\Bibitem{PolHen86}
\by P.~L.~Polyakov, G.~M.~Henkin
\paper Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the Radon--Penrose transform
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 566--597
\mathnet{http://mi.mathnet.ru/izv1501}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854596}
\zmath{https://zbmath.org/?q=an:0624.32004|0607.32003}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 555--587
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000898}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. Yu. Sternin, V. E. Shatalov, “Differential equations on complex-analytic manifolds, and the Maslov canonical operator”, Russian Math. Surveys, 43:3 (1988), 117–148  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. D'Agnolo A., Marastoni C., “Real Forms of the Radon-Penrose Transform”, Publ. Res. Inst. Math. Sci., 36:3 (2000), 337–383  crossref  mathscinet  isi
    3. Andrei Iordan, Fanny Matthey, “Régularité de l'opérateur et théorème de Siu sur la non-existence d'hypersurfaces Levi-plates dans l'espace projectif complexe”, Comptes Rendus Mathematique, 346:7-8 (2008), 395  crossref
    4. G. M. Henkin, R. G. Novikov, “On the Reconstruction of Conductivity of a Bordered Two-dimensional Surface in ℝ3 from Electrical Current Measurements on Its Boundary”, J Geom Anal, 2010  crossref
    5. Gennadi M. Henkin, Peter L. Polyakov, “Residual
      $${\bar\partial}$$
      -cohomology and the complex Radon transform on subvarieties of
      $${\mathbb C P^n}$$
      ”, Math. Ann, 2011  crossref
    6. QianQian Kang, Wei Wang, “On Radon-Penrose transformation and k-Cauchy-Fueter operator”, Sci. China Math, 2012  crossref
    7. Proc. Steklov Inst. Math., 279 (2012), 230–244  mathnet  crossref  mathscinet  isi  elib
    8. B. Berndtsson, S. V. Kislyakov, R. G. Novikov, V. M. Polterovich, P. L. Polyakov, A. E. Tumanov, A. A. Shananin, C. L. Epstein, “Gennadi Markovich Henkin (obituary)”, Russian Math. Surveys, 72:3 (2017), 547–570  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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