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An improvement of the Liouville theorem for discrete harmonic functions on $\mathbb{Z}^2$ is obtained.
J. Capoulade, Sur Quelques propiétés des fonctions harmoniques et des fonctions préharmoniques
1932
Earlier work this paper cites.
E. J. Remez, Sur une propriété des polynômes de Tchebyscheff
1936
Earlier work this paper cites.
H. A. Heilbronn, On discrete harmonic functions
1949
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M. de Guzman, Differentiation of integrals in ℝ n \mathbb{R}^{n} , Lecture Notes in Mathematics 481, Springer, 1975
1975
Cited alongside, same era.
N. S. Nadirashvili, Estimation of the solutions of elliptic equations with analytic coefficients which are bounded on some set
1979
Cited alongside, same era.
B. Bojanov, Elementary proof of the Remez Inequality
1993
Cited alongside, same era.
A. Eremenko, Mathoverflow, www.mathoverflow.net/questions/190837/entire-function-bounded-at-every-line
Cited in the paper.
G. Pólya, G. Szegö, Problems and Theorems in Analysis I, Classics in Mathematics, vol. 193, Springer, 1998
1998
Later among the works it cites.
T. Tao, An Introduction to Measure Theory, Graduate Studies in Math., vol. 126, AMS, 2011
2011
Later among the works it cites.
M. Guadie, E. Malinnikova, On three balls theorem for discrete harmonic functions
2014
Later among the works it cites.
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