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Meyer Points and Refined Meyer Points for Arbitrary Harmonic Functions

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Abstract

In this paper, the Meyer points and the refined Meyer points for arbitrary harmonic functions defined in a unit circle are studied. The representation of points which belong to set M( f ) is also considered.

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REFERENCES

  1. I. I. Privalov, Boundary Properties of Analytic Functions (GITTL, Moscow, 1950) [in Russian].

    Google Scholar 

  2. K. Nosiro, Cluster Sets (Springer, Berlin, 1960). https://doi.org/10.1007/978-3-642-85928-1

  3. E. D. Solomentsev, “Harmonic and subharmonic functions and their generalizations,” in Results of Science: Ser. Mathematical Analysis, Probability Theory, Control 1962 (VINITI Akad. Nauk SSSR, Moscow, 1964), vol. 1, pp. 83–100.

    Google Scholar 

  4. E. Collingwood and A. Lohwater, The Theory of Cluster Sets (Cambridge Univ. Press, Cambridge, 1966).

  5. V. I. Gavrilov and V. S. Zakharyan, “Set of Lindelöf points of arbitrary complex functions,” Dokl. Akad. Nauk Arm. SSR 86 (1), 12–16 (1988).

    MATH  Google Scholar 

  6. V. I. Gavrilov, V. S. Zakharyan, and A. V. Subbotin, “ Linear topological properties of maximal Hardy spaces of functions harmonic in the disk,” Dokl. Nats. Akad. Nauk Arm. 102 (3), 203–209 (2002).

    MathSciNet  Google Scholar 

  7. S. L. Berberyan, “On some types of boundary points of harmonic functions,” Russ. Math. 58 (5), 1–7 (2014). https://doi.org/10.3103/S1066369X14050016

    Article  MathSciNet  MATH  Google Scholar 

  8. S. L. Berberyan and V. I. Gavrilov, “Limit sets of continuous and harmonic functions along nontangent boundary paths,” Math. Montisnigri 1, 17–25 (1993).

    MathSciNet  Google Scholar 

  9. Sh. Yamashita, “On Fatou- and Plessner-type theorems,” Proc. Jpn. Acad. 46 (6), 494–495 (1970). https://doi.org/10.3792/pja/1195520262

    Article  MathSciNet  MATH  Google Scholar 

  10. S. L. Berberyan, “The distribution of values of harmonic functions in the unit disk,” Russ. Math. 55 (6), 9–14 (2011). https://doi.org/10.3103/S1066369X11060028

    Article  MathSciNet  MATH  Google Scholar 

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Funding

The study was carried out with financial support in the framework of the development program of the Russian-Armenian University.

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Authors and Affiliations

  1. Russian-Armenian (Slavonic) University, 0051, Yerevan, Republic of Armenia

    S. L. Berberyan

Authors
  1. S. L. Berberyan
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Correspondence to S. L. Berberyan.

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The author declares that he has no conflicts of interest.

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Translated by A.V. Shishulin

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Berberyan, S.L. Meyer Points and Refined Meyer Points for Arbitrary Harmonic Functions. Russ Math. 66, 21–25 (2022). https://doi.org/10.3103/S1066369X22050024

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  • DOI: https://doi.org/10.3103/S1066369X22050024

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