scholarly journals Correction to: Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions

2019 ◽  
Vol 71 (6) ◽  
pp. 984-984
Author(s):  
A. S. Serdyuk ◽  
I. V. Sokolenko
Keyword(s):  
Entire Functions ◽  
Trigonometric Polynomials ◽  
The Space Lp ◽  
Interpolation Trigonometric

Inequalities for Entire Functions of Exponential Type

1984 ◽  
Vol 27 (4) ◽  
pp. 463-471 ◽  
Author(s):  
Clément Frappier
Keyword(s):  
Entire Function ◽  
Real Axis ◽  
Exponential Type ◽  
Entire Functions ◽  
Indicator Function ◽  
Trigonometric Polynomials ◽  
Bernstein’S Inequality ◽  
The Real ◽  
Functions Of Exponential Type ◽  
Image Position

AbstractBernstein's inequality says that if f is an entire function of exponential type τ which is bounded on the real axis thenGenchev has proved that if, in addition, hf (π/2) ≤0, where hf is the indicator function of f, thenUsing a method of approximation due to Lewitan, in a form given by Hörmander, we obtain, to begin, a generalization and a refinement of Genchev's result. Also, we extend to entire functions of exponential type two results first proved for polynomials by Rahman. Finally, we generalize a theorem of Boas concerning trigonometric polynomials vanishing at the origin.

scholarly journals Nikolskii-type inequalities for trigonometric polynomials and entire functions of exponential type

1978 ◽  
Vol 25 (1) ◽  
pp. 7-18 ◽  
Author(s):  
R. J. Nessel ◽  
G. Wilmes
Keyword(s):  
Fourier Transform ◽  
Exponential Type ◽  
Compact Support ◽  
Entire Functions ◽  
Symmetric Body ◽  
Trigonometric Polynomials ◽  
Several Variables ◽  
Integrable Functions ◽  
Functions Of Exponential Type

AbstractNikolskii-type inequalities, thus inequalities between different metrics of a function, are established for trigonometric polynomials and pth power integrable functions, 0<p<∞, of several variables having Fourier transform with compact support. It is shown that certain gaps in the spectra of the functions involved may be taken into account. As an immediate consequence it follows that the general results cover the classical inequalities which are concerned with functions of rectangular type. But at the same time one may give applications to functions of type K where K is a symmetric body in Euclidean n–space.

Sign in / Sign up

Export Citation Format

Share Document