Displaying similar documents to “The nonlinear superposition operator acting on Bergman spaces”

On approximation and interpolation of entire functions with index-pair (p,q).

H. S. Kasana, Devendra Kumar (1994)

Publicacions Matemàtiques

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In this paper we have studied the Chebyshev and interpolation errors for functions in C(E), the normed algebra of analytic functions on a compact set E of positive transfinite diameter. The (p,q)-order and generalized (p,q)-type have been characterized in terms of these approximation errors. Finally, we have obtained a saturation theorem for f ∈ C(E) which can be extended to an entire function of (p,q)-order 0 or 1 and for entire functions of minimal generalized (p,q)-type.

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

Xiao-Min Li, Hong-Xun Yi (2009)

Czechoslovak Mathematical Journal

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We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.

The deficiency of entire functions with Fejér gaps

Takafumi Murai (1983)

Annales de l'institut Fourier

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We say that an entire function f ( z ) = ∑ k = 0 a k z n k ( 0 = n 0 < n 1 < n 2 < ... ) has Fejér gaps if ∑ k = 1 ∞ 1 / n k < ∞ . The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.