scholarly journals Entire functions in several variables with constant absolute values on a circular uniqueness set

1962 ◽  
Vol 13 (1) ◽  
pp. 117-117 ◽  
Author(s):  
S. Bochner
Keyword(s):  
Entire Functions ◽  
Several Variables ◽  
Uniqueness Set

scholarly journals Approximation characteristics of the isotropic Nikol'skii-Besov functional classes

2021 ◽  
Vol 13 (3) ◽  
pp. 851-861
Author(s):  
S.Ya. Yanchenko ◽  
O.Ya. Radchenko
Keyword(s):  
Exponential Type ◽  
Lebesgue Space ◽  
Entire Functions ◽  
Exact Order ◽  
Periodic Functions ◽  
Approximation Of Functions ◽  
Several Variables ◽  
Functions Of Exponential Type ◽  
Functional Classes ◽  
Mixed Smoothness

In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,\theta}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p,\theta}B(\mathbb{R})$. We establish the exact-order estimates for the approximation of functions from these classes $B^r_{p,\theta}(\mathbb{R}^d)$ in the metric of the Lebesgue space $L_q(\mathbb{R}^d)$, by entire functions of exponential type with some restrictions for their spectrum in the case $1 \leqslant p \leqslant q \leqslant \infty$, $(p,q)\neq \{(1,1), (\infty, \infty)\}$, $d\geq 1$. In the case $2<p=q<\infty$, $d=1$, the established estimate is also new for the classes $S^{r}_{p,\theta}B(\mathbb{R})$.

Reconstruction of Entire Functions From Irregularly Spaced Sample Points

1996 ◽  
Vol 48 (4) ◽  
pp. 777-793 ◽  
Author(s):  
Georgi R. Grozev ◽  
Qazi I. Rahman
Keyword(s):  
Entire Functions ◽  
Constant Independent ◽  
Real Numbers ◽  
Several Variables ◽  
Derivative Sampling ◽  
Sample Points

AbstractLet where {λn}n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ ℤ . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.

scholarly journals Approximation of a Function and its Derivatives by Entire Functions of Several Variables

1988 ◽  
Vol 31 (4) ◽  
pp. 495-499 ◽  
Author(s):  
El Mostapha Frih ◽  
Paul M. Gauthier
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Several Variables ◽  
Approximation Of A Function

AbstractThe paper gives a good approximation of a Ck function on Rn and its derivatives by the restriction of an entire function on Cn and its derivatives respectively.

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