Approximation of ultra-differentiable functions by polynomials and entire functions

1984 ◽  
Vol 48 (1-3) ◽  
pp. 227-250 ◽  
Author(s):  
Hans -Joachim Petzsche
Keyword(s):  
Entire Functions ◽  
Differentiable Functions

scholarly journals On the best mean-square approximation by entire functions of finite type on the line

2021 ◽  
Vol 17 ◽  
pp. 36
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Finite Type ◽  
Entire Functions ◽  
Jackson Type ◽  
Mean Square ◽  
Differentiable Functions

Jackson-type inequalities have been obtained for the best mean square approximation of differentiable functions by means of the entire functions of finite type on the line.

scholarly journals Sharp estimates of approximation of classes of differentiable functions by entire functions

2021 ◽  
pp. 3
Author(s):  
V.F. Babenko ◽  
A.Yu. Gromov
Keyword(s):  
Exponential Type ◽  
Best Approximation ◽  
Entire Functions ◽  
Sharp Estimate ◽  
Sharp Estimates ◽  
The Best Approximation ◽  
Differentiable Functions ◽  
Functions Of Exponential Type

In the paper, we find the sharp estimate of the best approximation, by entire functions of exponential type not greater than $\sigma$, for functions $f(x)$ from the class $W^r H^{\omega}$ such that $\lim\limits_{x \rightarrow -\infty} f(x) = \lim\limits_{x \rightarrow \infty} f(x) = 0$,$$A_{\sigma}(W^r H^{\omega}_0)_C = \frac{1}{\sigma^{r+1}} \int\limits_0^{\pi} \Phi_{\pi, r}(t)\omega'(t/\sigma)dt$$for $\sigma > 0$, $r = 1, 2, 3, \ldots$ and concave modulus of continuity.Also, we calculate the supremum$$\sup\limits_{\substack{f\in L^{(r)}\\f \ne const}} \frac{\sigma^r A_{\sigma}(f)_L}{\omega (f^{(r)}, \pi/\sigma)_L} = \frac{K_L}{2}$$

Differentiable Functions Have Sparse Graphs

1978 ◽  
Vol 4 (1) ◽  
pp. 91
Author(s):  
Laczkovich ◽  
Petruska
Keyword(s):  
Sparse Graphs ◽  
Differentiable Functions

Rate of approximation of entire functions by a complete Dirichlet system

1984 ◽  
Vol 36 (6) ◽  
pp. 928-931
Author(s):  
V. Kh. Musoyan
Keyword(s):  
Entire Functions ◽  
Rate Of Approximation
Sign in / Sign up

Export Citation Format

Share Document