scholarly journals A new characterization of entire functions of completely regular growth

1981 ◽  
Vol 81 (2) ◽  
pp. 308-319 ◽  
Author(s):  
Mark S Ephron
Keyword(s):  
Entire Functions ◽  
Regular Growth ◽  
Completely Regular

Deficient values of entire functions of completely regular growth along curves of regular rotation

1982 ◽  
Vol 31 (1) ◽  
pp. 8-14
Author(s):  
S. K. Balashov ◽  
G. Opitz ◽  
A. I. Heifits
Keyword(s):  
Entire Functions ◽  
Regular Growth ◽  
Completely Regular

scholarly journals SOME ESTIMATES OF SPECIAL CLASSES OF INTEGRALS

2000 ◽  
Vol 5 (1) ◽  
pp. 127-132
Author(s):  
T. I. Malyutina
Keyword(s):  
Asymptotic Formula ◽  
Asymptotic Expansions ◽  
Entire Functions ◽  
Regular Growth ◽  
Asymptotic Formulas ◽  
Arbitrary Parameter ◽  
Subharmonic Functions ◽  
Completely Regular ◽  
Asymptotic Formulae ◽  
New Variant

We study the integrals fb a f(t) exp(i| ln rt|σ) dt and obtain asymptotic formula for these functions of non‐regular growth. This is a peculiar kind of the theory asymptotic expansions. In particular, we get asymptotic formulae for different entire functions of non‐regular growth. Asymptotic formulas for Levin‐Pfluger entire functions of completely regular growth are well‐known [1]. Our formulas allow to find limiting Azarin's [2] sets for some subharmonic functions. The kernel exp(i| ln rt|σ) contains arbitrary parameter σ > 0. The integrals for σ ∈(0, 1), σ = 1, σ > 1 essentially differ. Our arguments can apply to more general kernels. We give a new variant of the classic lemma of Riemann and Lebesgue from the theory of the transformation of Fourier.

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