scholarly journals Polynomial approximation to harmonic and analytic functions: generalized continuity conditions

1950 ◽  
Vol 68 (2) ◽  
pp. 183-183 ◽  
Author(s):  
J. L. Walsh ◽  
H. Margaret Elliott
Keyword(s):  
Polynomial Approximation ◽  
Analytic Functions ◽  
Generalized Continuity ◽  
Harmonic And Analytic Functions

scholarly journals Polynomial Approximation of Anisotropic Analytic Functions of Several Variables

2020 ◽  
Author(s):  
Andrea Bonito ◽  
Ronald DeVore ◽  
Diane Guignard ◽  
Peter Jantsch ◽  
Guergana Petrova
Keyword(s):  
Polynomial Approximation ◽  
Analytic Functions ◽  
Several Variables

scholarly journals On uniform polynomial approximation of functions that are analytic in finite number of non-intersecting continuums

2021 ◽  
Vol 16 ◽  
pp. 41
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk ◽  
V.I. Zabutna
Keyword(s):  
Finite Number ◽  
Polynomial Approximation ◽  
Analytic Functions ◽  
Function Theory ◽  
Approximation Of Functions ◽  
Constructive Function ◽  
Asymptotic Values ◽  
Uniform Polynomial Approximation ◽  
Polynomial Approximation Of Functions

We show that some of results, obtained by S.N. Bernstein, on constructive function theory, under certain conditions, take place for uniform polynomial approximation of functions that are analytic in finite number of non-intersecting continuums. On the base of obtained results for certain class of analytic functions we calculate asymptotic values of some $n$-widths.

scholarly journals The best polynomial approximations of some classes of analytic functions in the Hardy spaces

2018 ◽  
Vol 26 (1) ◽  
pp. 8 ◽  
Author(s):  
S.B. Vakarchuk ◽  
V.I. Zabutna ◽  
M.B. Vakarchuk
Keyword(s):  
Polynomial Approximation ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Best Polynomial Approximation ◽  
Polynomial Approximations ◽  
Methods Of Approximation

Problems of the best polynomial approximation of classes of analytic functions $$$H^m_{p,R}$$$, $$$m\in \mathbb{Z}_+$$$, $$$R \geqslant 1$$$, $$$1 \leqslant p \leqslant \infty$$$, have been investigated in the Hardy spaces $$$H_p$$$. The best linear methods of approximation were constructed on the indicated classes.

scholarly journals On Level Curves of Harmonic and Analytic Functions on Riemann Surfaces

1969 ◽  
Vol 34 ◽  
pp. 77-87
Author(s):  
Shinji Yamashitad
Keyword(s):  
Riemann Surface ◽  
Subharmonic Function ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Vector Lattice ◽  
Level Curves ◽  
Harmonic Majorant ◽  
Harmonic And Analytic Functions ◽  
Hyperbolic Riemann Surface

In this note we shall denote by R a hyperbolic Riemann surface. Let HP′(R) be the totality of harmonic functions u on R such that every subharmonic function | u | has a harmonic majorant on R. The class HP′(R) forms a vector lattice under the lattice operations:

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