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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 4, Pages 905–925 (Mi smj1222)  

This article is cited in 18 scientific papers (total in 18 papers)

Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions

B. N. Khabibullin

Bashkir State University
References:
Abstract: We obtain criteria for harmonicity and subharmonicity of a function in a domain in Rd, d2, in terms of special Arens–Singer and Jensen measures. We also establish a criterion for (sub-)harmonicity of a δ-subharmonic function in terms of the associated Riesz charge and special Arens–Singer and Jensen functions. To this end, we use the theorem of this article on continuation of (sub-)harmonic functions to polar sets.
Keywords: harmonic function, subharmonic function, Jensen measure, Arens–Singer measure.
Received: 14.08.2001
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 4, Pages 713–728
DOI: https://doi.org/10.1023/A:1024796809786
Bibliographic databases:
UDC: 517.574
Language: Russian
Citation: B. N. Khabibullin, “Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions”, Sibirsk. Mat. Zh., 44:4 (2003), 905–925; Siberian Math. J., 44:4 (2003), 713–728
Citation in format AMSBIB
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\paper Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
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\pages 905--925
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2010135}
\zmath{https://zbmath.org/?q=an:1030.31004}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 4
\pages 713--728
\crossref{https://doi.org/10.1023/A:1024796809786}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000184886500016}
Linking options:
  • https://www.mathnet.ru/eng/smj1222
  • https://www.mathnet.ru/eng/smj/v44/i4/p905
  • This publication is cited in the following 18 articles:
    1. B. N. Khabibullin, E. U. Taipova, “Lower Estimates for Subhramonic Functions and the Harnack Distance”, J Math Sci, 260:6 (2022), 833  crossref
    2. B. N. Khabibullin, E. B. Menshikova, “Preorders on Subharmonic Functions and Measures with Applications to the Distribution of Zeros of Holomorphic Functions”, Lobachevskii J Math, 43:3 (2022), 587  crossref
    3. B. N. Khabibullin, “Poisson–Jensen formulas and balayage of measures”, Eurasian Math. J., 12:4 (2021), 53–73  mathnet  crossref
    4. Khabibullin B.N., Menshikova E.B., “Balayage of Measures With Respect to Polynomials and Logarithmic Kernels on the Complex Plane”, Lobachevskii J. Math., 42:12 (2021), 2823–2833  crossref  mathscinet  zmath  isi  scopus
    5. Khabibullin B.N., Khabibullin F.B., “Necessary and Sufficient Conditions For Zero Subsets of Holomorphic Functions With Upper Constraints in Planar Domains”, Lobachevskii J. Math., 42:4, SI (2021), 800–810  crossref  mathscinet  zmath  isi  scopus
    6. E. B. Menshikova, B. N. Khabibullin, “A criterion for the sequence of roots of holomorphic function with restrictions on its growth”, Russian Math. (Iz. VUZ), 64:5 (2020), 49–55  mathnet  crossref  crossref  isi
    7. Khabibullin B.N., “Balayage of Measures With Respect to (Sub-)Harmonic Functions”, Lobachevskii J. Math., 41:11, SI (2020), 2179–2189  crossref  mathscinet  zmath  isi  scopus
    8. E. B. Menshikova, B. N. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. II”, Funkts. analiz i ego pril., 53:1 (2019), 84–87  mathnet  crossref  mathscinet  elib
    9. B. N. Khabibullin, F. B. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. III. Teoremy obrascheniya”, Funkts. analiz i ego pril., 53:2 (2019), 42–58  mathnet  crossref  mathscinet  elib
    10. B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funct. Anal. Appl., 52:1 (2018), 21–34  mathnet  crossref  crossref  mathscinet  isi  elib
    11. Khabibullin B.N., Tamindarova N.R., “Uniqueness Theorems For Subharmonic and Holomorphic Functions of Several Variables on a Domain”, Azerbaijan J. Math., 7:1 (2017), 70–78  mathscinet  zmath  isi
    12. T. Yu. Bayguskarov, G. R. Talipova, B. N. Khabibullin, “Subsequences of zeros for classes of entire functions of exponential type, allocated by restrictions on their growth”, St. Petersburg Math. J., 28:2 (2017), 127–151  mathnet  crossref  mathscinet  isi  elib
    13. Hansen W., Netuka I., “Jensen Measures in Potential Theory”, Potential Anal., 37:1 (2012), 79–90  crossref  mathscinet  zmath  isi  scopus
    14. Lin Dai, Weifeng Zhang, 2011 International Conference on Multimedia Technology, 2011, 2362  crossref
    15. E. G. Kudasheva, B. N. Khabibullin, “The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions there”, Sb. Math., 200:9 (2009), 1353–1382  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. B. N. Khabibullin, F. B. Khabibullin, L. Yu. Cherednikova, “Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. I”, St. Petersburg Math. J., 20:1 (2009), 101–129  mathnet  crossref  mathscinet  zmath  isi
    17. B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants”, Sb. Math., 198:2 (2007), 261–298  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. B. N. Khabibullin, “Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disc”, Sb. Math., 197:2 (2006), 259–279  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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