This article is cited in 2 scientific papers (total in 2 papers)
Generalization of a theorem of Men'shov on monogenic functions
D. S. Telyakovskii
It is shown that in Men'shov's theorem on the holomorphicity of continuous functions monogenic at each point of a domain with respect to two intervals intersecting at this point the condition of continuity of $f(z)$ may be replaced by the condition of summability of $(\log^+|f(z)|)^p$ for all positive $p<2$. As
a collateral result a theorem of Phragmén–Lindelöf type is proved in which
a certain summability condition is imposed in place of a condition on the growth of the function.
Bibliography: 17 titles.
PDF file (1275 kB)
Mathematics of the USSR-Izvestiya, 1990, 35:1, 221–231
D. S. Telyakovskii, “Generalization of a theorem of Men'shov on monogenic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 886–896; Math. USSR-Izv., 35:1 (1990), 221–231
Citation in format AMSBIB
\paper Generalization of a~theorem of Men'shov on monogenic functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
E. P. Dolzhenko, “The work of D. E. Men'shov in the theory of analytic functions and the present state of the theory of monogeneity”, Russian Math. Surveys, 47:5 (1992), 71–102
D. S. Telyakovskii, “A Generalization of Men'shov's Theorem on Functions Satisfying Condition $K"$”, Math. Notes, 76:4 (2004), 534–545
|Number of views:|