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Search: All articles in the CMB digital archive with keyword entire function

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1. CMB Online first

Li, Bao Qin
An Equivalent Form of Picard's Theorem and Beyond
This paper gives an equivalent form of Picard's theorem via entire solutions of the functional equation $f^2+g^2=1$, and then its improvements and applications to certain nonlinear (ordinary and partial) differential equations.

Keywords:entire function, Picard's Theorem, functional equation, partial differential equation
Categories:30D20, 32A15, 35F20

2. CMB 2012 (vol 56 pp. 769)

Lahiri, Indrajit; Kaish, Imrul
A Non-zero Value Shared by an Entire Function and its Linear Differential Polynomials
In this paper we study uniqueness of entire functions sharing a non-zero finite value with linear differential polynomials and address a result of W. Wang and P. Li.

Keywords:entire function, linear differential polynomial, value sharing

3. CMB 2009 (vol 53 pp. 11)

Burke, Maxim R.
Approximation and Interpolation by Entire Functions of Several Variables
Let $f\colon \mathbb R^n\to \mathbb R$ be $C^\infty$ and let $h\colon \mathbb R^n\to\mathbb R$ be positive and continuous. For any unbounded nondecreasing sequence $\{c_k\}$ of nonnegative real numbers and for any sequence without accumulation points $\{x_m\}$ in $\mathbb R^n$, there exists an entire function $g\colon\mathbb C^n\to\mathbb C$ taking real values on $\mathbb R^n$ such that \begin{align*} &|g^{(\alpha)}(x)-f^{(\alpha)}(x)|\lt h(x), \quad |x|\ge c_k, |\alpha|\le k, k=0,1,2,\dots, \\ &g^{(\alpha)}(x_m)=f^{(\alpha)}(x_m), \quad |x_m|\ge c_k, |\alpha|\le k, m,k=0,1,2,\dots. \end{align*} This is a version for functions of several variables of the case $n=1$ due to L. Hoischen.

Keywords:entire function, complex approximation, interpolation, several complex variables

4. CMB 2008 (vol 51 pp. 378)

Izuchi, Kou Hei
Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions
In this paper, we generalize a result recently obtained by the author. We characterize the cyclic vectors in $\Lp$. Let $f\in\Lp$ and $f\poly$ be contained in the space. We show that $f$ is non-vanishing if and only if $f$ is cyclic.

Keywords:weighted $L^p$ spaces of entire functions, cyclic vectors
Categories:47A16, 46J15, 46H25

5. CMB 2005 (vol 48 pp. 161)

Betancor, Jorge J.
Hankel Convolution Operators on Spaces of Entire Functions of Finite Order
In this paper we study Hankel transforms and Hankel convolution operators on spaces of entire functions of finite order and their duals.

Keywords:Hankel transform, convolution, entire functions, finite order

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