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Mathematics of the USSR-Sbornik, 1976, Volume 30, Issue 4, Pages 501–514
DOI: https://doi.org/10.1070/SM1976v030n04ABEH002285
(Mi sm2914)
 

This article is cited in 28 scientific papers (total in 28 papers)

A boundary uniqueness theorem in Cn

A. S. Sadullaev
References:
Abstract: The classical boundary theorem of F. and M. Riesz asserts that, if the radial limits of a bounded holomorphic function f(z) in the disk |z|<1 lie in a set of capacity zero for a set of positive measure on the circle |z|=1, then f(z)constant. The main result of this paper is the proof of an analogous theorem for maps F:DCn, where D is a domain in Cn. We take as uniqueness set on the boundary any set of positive Lebesgue measure on a generating submanifold.
Bibliography: 12 titles.
Received: 09.10.1975
Bibliographic databases:
UDC: 517.55
MSC: Primary 31C10, 31B25; Secondary 32A10, 32F05
Language: English
Original paper language: Russian
Citation: A. S. Sadullaev, “A boundary uniqueness theorem in Cn”, Math. USSR-Sb., 30:4 (1976), 501–514
Citation in format AMSBIB
\Bibitem{Sad76}
\by A.~S.~Sadullaev
\paper A~boundary uniqueness theorem in~$\mathbf C^n$
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 4
\pages 501--514
\mathnet{http://mi.mathnet.ru/eng/sm2914}
\crossref{https://doi.org/10.1070/SM1976v030n04ABEH002285}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=486622}
\zmath{https://zbmath.org/?q=an:0346.32024}
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Linking options:
  • https://www.mathnet.ru/eng/sm2914
  • https://doi.org/10.1070/SM1976v030n04ABEH002285
  • https://www.mathnet.ru/eng/sm/v143/i4/p568
  • This publication is cited in the following 28 articles:
    1. Ufa Math. J., 14:3 (2022), 127–140  mathnet  crossref  mathscinet
    2. Sadullaev A., Zeriahi A., “Subsets of Full Measure in a Generic Submanifold in C-N Are Non-Plurithin”, Math. Z., 274:3-4 (2013), 1155–1163  crossref  mathscinet  zmath  isi
    3. Ashurov R., Butaev A., “The Kahane Theorem for Nonspherical Partial Sums of Fourier Integrals”, C. R. Math., 348:19-20 (2010), 1103–1106  crossref  mathscinet  zmath  isi
    4. Pujals E.R., Roeder R.K.W., “Two-Dimensional Blaschke Products: Degree Growth and Ergodic Consequences”, Indiana Univ. Math. J., 59:1 (2010), 301–325  crossref  mathscinet  isi  elib
    5. Armen Edigarian, Jan Wiegerinck, “Shcherbina’s theorem for finely holomorphic functions”, Math Z, 2009  crossref  mathscinet
    6. A. A. Atamuratov, “On Meromorphic Continuation in a Fixed Direction”, Math. Notes, 86:3 (2009), 301–305  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Eroshkin O., “Pluripolarity of Manifolds”, Banach Spaces of Analytic Functions, Contemporary Mathematics Series, 454, eds. Hibschweiler R., MacGregor T., Amer Soc Mechanical Engineers, 2008, 23–33  crossref  mathscinet  zmath  isi
    8. A. S. Sadullaev, S. A. Imomkulov, “Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections”, Proc. Steklov Inst. Math., 253 (2006), 144–159  mathnet  crossref  mathscinet  zmath
    9. S. A. Imomkulov, “On holomorphic continuation of functions defined on a pencil of boundary complex lines”, Izv. Math., 69:2 (2005), 345–363  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Coman D., Levenberg N., Poletsky E., “Smooth Submanifolds Intersecting Any Analytic Curve in a Discrete Set”, Math. Ann., 332:1 (2005), 55–65  crossref  mathscinet  zmath  isi
    11. A. B. Sukhov, “On continuous extension and rigidity of holomorphic mappings between domains with piecewise smooth boundaries”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 471–483  mathnet  crossref  mathscinet  zmath  isi
    12. Forstneric F., “A Reflection Principle on Strongly Pseudoconvex Domains with Generic Corners”, Math. Z., 213:1 (1993), 49–64  crossref  mathscinet  zmath  isi
    13. Bernard Coupet, “Construction de disques analytiques et régularité defonctions holomorphes au bord”, Math Z, 209:1 (1992), 179  crossref  mathscinet  zmath  isi
    14. Franc Forstnerič, “Mappings of quadric Cauchy-Riemann manifolds”, Math Ann, 292:1 (1992), 163  crossref  mathscinet  zmath  isi
    15. Alinhac S. Baouendi M. Rothschild L., “Unique Continuation and Regularity at the Boundary for Holomorphic-Functions”, Duke Math. J., 61:2 (1990), 635–653  crossref  mathscinet  zmath  isi
    16. Aizenberg L., Tarkhanov N., “Abstract Carleman Formula”, 298, no. 6, 1988, 1292–1296  mathscinet  isi
    17. E. O. Nazaryan, “O mnogomernom analoge formuly Karlemana, imeyuschem golomorfnoe yadro”, Uch. zapiski EGU, ser. Fizika i Matematika, 1988, no. 1, 147–149  mathnet
    18. Coupet B., “Construction of Analytic Disks and Applications”, Comptes Rendus Acad. Sci. Ser. I-Math., 304:14 (1987), 427–430  mathscinet  zmath  isi
    19. Jacques Chaumat, Anne-Marie Chollet, “Dimension de Hausdorff des ensembles de zéros et d'interpolation pour 𝐴^{∞}(𝐷)”, Trans. Amer. Math. Soc., 299:1 (1987), 95  crossref
    20. Joseph A. Cima, Emil J. Straube, “Boundary uniqueness theorems in 𝐶ⁿ”, Trans. Amer. Math. Soc., 294:1 (1986), 333  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:59
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