scholarly journals Uniform polynomial approximation and generalized growth of entire functions on arbitrary compact sets

2009 ◽  
Vol 16 (2) ◽  
pp. 265-276
Author(s):  
G.S. Srivastava
Keyword(s):  
Polynomial Approximation ◽  
Entire Functions ◽  
Compact Sets ◽  
Growth Of Entire Functions ◽  
Uniform Polynomial Approximation

scholarly journals Generalized Order and Best Approximation of Entire Function in -Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mohammed Harfaoui
Keyword(s):  
Entire Function ◽  
Polynomial Approximation ◽  
Best Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Best Polynomial Approximation ◽  
Growth Of Entire Functions

The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact with respect to the set , where is the Siciak extremal function of a -regular compact .

scholarly journals Best Polynomial Approximation in -Norm and -Growth of Entire Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed El Kadiri ◽  
Mohammed Harfaoui
Keyword(s):  
Continuous Function ◽  
Polynomial Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Maximum Norm ◽  
Best Polynomial Approximation ◽  
General Growth ◽  
Growth Of Entire Functions ◽  
Approximation Errors ◽  
Positive Capacity

The classical growth has been characterized in terms of approximation errors for a continuous function on by Reddy (1970), and a compact of positive capacity by Nguyen (1982) and Winiarski (1970) with respect to the maximum norm. The aim of this paper is to give the general growth (-growth) of entire functions in by means of the best polynomial approximation in terms of -norm, with respect to the set , where is the Siciak's extremal function on an -regular nonpluripolar compact is not pluripolar.

Algebraic Values of Entire Functions with Extremal Growth Orders: An Extension of a Theorem of Boxall and Jones

2019 ◽  
Vol 63 (3) ◽  
pp. 536-546
Author(s):  
Taboka Prince Chalebgwa
Keyword(s):  
Entire Function ◽  
Finite Order ◽  
Lower Order ◽  
Entire Functions ◽  
Compact Sets ◽  
Bounded Degree ◽  
Growth Of Entire Functions ◽  
Original Theorem

AbstractGiven an entire function $f$ of finite order $\unicode[STIX]{x1D70C}$ and positive lower order $\unicode[STIX]{x1D706}$, Boxall and Jones proved a bound of the form $C(\log H)^{\unicode[STIX]{x1D702}(\unicode[STIX]{x1D706},\unicode[STIX]{x1D70C})}$ for the density of algebraic points of bounded degree and height at most $H$ on the restrictions to compact sets of the graph of $f$. The constant $C$ and exponent $\unicode[STIX]{x1D702}$ are effectively computable from certain data associated with the function. In this followup note, using different measures of the growth of entire functions, we obtain similar bounds for other classes of functions to which the original theorem does not apply.

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