Generalized Order and Best Approximation of Entire Function in 𝐿𝑝-Norm
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 𝐾 with respect to the set Ω𝑟={𝑧∈𝐂𝑛;exp𝑉𝐾(𝑧)≤𝑟}, where 𝑉𝐾=sup{(1/𝑑)ln|𝑃𝑑|,𝑃𝑑polynomialofdegree≤𝑑,‖𝑃𝑑‖𝐾≤...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/360180 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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 𝐾 with respect to the set Ω𝑟={𝑧∈𝐂𝑛;exp𝑉𝐾(𝑧)≤𝑟}, where 𝑉𝐾=sup{(1/𝑑)ln|𝑃𝑑|,𝑃𝑑polynomialofdegree≤𝑑,‖𝑃𝑑‖𝐾≤1} is the Siciak extremal function of a 𝐿-regular compact 𝐾. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |