The Converse Fatou Theorem for Smooth Measures

2006 ◽  
Vol 134 (4) ◽  
pp. 2288-2291
Author(s):  
E. S. Dubtsov
Keyword(s):  
Fatou Theorem ◽  
Smooth Measures

On the fatou theorem for p-harmonic function

1988 ◽  
Vol 13 (6) ◽  
pp. 651-668 ◽  
Author(s):  
Juan J. Manfredi ◽  
Allen Weitsman
Keyword(s):  
Harmonic Function ◽  
Fatou Theorem

On a Theorem of Hayman Concerning Quasi-Bounded Functions

1959 ◽  
Vol 11 ◽  
pp. 593-600
Author(s):  
P. B. Kennedy
Keyword(s):  
Meromorphic Functions ◽  
Bounded Function ◽  
Fatou Theorem ◽  
Regular Functions ◽  
Bounded Functions ◽  
Image Position ◽  
Special Case

If f(z) is regular in |z| < 1, the expressionis called the characteristic of f(z). This is the notation of Nevanlinna (4) for the special case of regular functions; in this note it will not be necessary to discuss meromorphic functions. If m(r,f) is bounded for 0 < r < 1, then f(z) is called quasi-bounded in |z| < 1. In particular, every bounded function is quasibounded. The class Q of quasi-bounded functions is important because, for instance, a “Fatou theorem” holds for such functions (4, p. 134).

Hahn-Jordan decomposition for smooth measures

1981 ◽  
Vol 30 (3) ◽  
pp. 710-712
Author(s):  
E. T. Shavgulidze
Keyword(s):  
Jordan Decomposition ◽  
Smooth Measures

A family of hyper-Bessel functions and convergent series in them

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Power Series ◽  
Bessel Function ◽  
Classical Theory ◽  
Bessel Functions ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Convergent Series ◽  
Multi Index ◽  
Fatou Theorem ◽  
Convergence Of Series

AbstractThe Delerue hyper-Bessel functions that appeared as a multi-index generalizations of the Bessel function of the first type, are closely related to the hyper-Bessel differential operators of arbitrary order, introduced by Dimovski. In this work we consider an enumerable family of hyper-Bessel functions and study the convergence of series in such a kind of functions. The obtained results are analogues to the ones in the classical theory of the widely used power series, like Cauchy-Hadamard, Abel and Fatou theorem.

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