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On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a finite number of singular points
N. V. Govorov, N. M. Chernykh
The following theorem is proved. Let $A(z)$ be an entire function of exponential type, and let its Borel transform $a(z)$ satisfy the following conditions: 1) $a(z)$ can be analytically continued to a certain Riemann surface $R$ with finite number of branch points, and it has only finitely many singularities $z_k$ on $R$; 2) in any plane with cuts by parallel rays issuing from the $z_k$, a branch of $z_k$ satisfies
Then $A(z)$ has completely regular growth. From this theorem it follows, in particular, that if
$a(z)$ is an algebraic function or a single-valued function with a finite number of singularities, then $A(z)$ has completely regular growth.
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Mathematics of the USSR-Izvestiya, 1979, 13:2, 253–259
N. V. Govorov, N. M. Chernykh, “On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a finite number of singular points”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 965–971; Math. USSR-Izv., 13:2 (1979), 253–259
Citation in format AMSBIB
\by N.~V.~Govorov, N.~M.~Chernykh
\paper On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a~finite number of singular points
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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This publication is cited in the following articles:
N. V. Govorov, N. M. Chernykh, “Complete regularity of growth for some classes of entire functions of exponential type represented by Вorel integrals and power series”, Math. USSR-Izv., 27:3 (1986), 431–450
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