Abstract:
We obtain criteria for harmonicity and subharmonicity of a function in a domain in Rd, d⩾2, 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.
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
This publication is cited in the following 18 articles:
B. N. Khabibullin, E. U. Taipova, “Lower Estimates for Subhramonic Functions and the Harnack Distance”, J Math Sci, 260:6 (2022), 833
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
B. N. Khabibullin, “Poisson–Jensen formulas and balayage of measures”, Eurasian Math. J., 12:4 (2021), 53–73
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
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
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
Khabibullin B.N., “Balayage of Measures With Respect to (Sub-)Harmonic Functions”, Lobachevskii J. Math., 41:11, SI (2020), 2179–2189
E. B. Menshikova, B. N. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. II”, Funkts. analiz i ego pril., 53:1 (2019), 84–87
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
B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funct. Anal. Appl., 52:1 (2018), 21–34
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
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
Hansen W., Netuka I., “Jensen Measures in Potential Theory”, Potential Anal., 37:1 (2012), 79–90
Lin Dai, Weifeng Zhang, 2011 International Conference on Multimedia Technology, 2011, 2362
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
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
B. N. Khabibullin, “Zero sequences of holomorphic functions, representation
of meromorphic functions, and harmonic minorants”, Sb. Math., 198:2 (2007), 261–298
B. N. Khabibullin, “Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disc”, Sb. Math., 197:2 (2006), 259–279
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