scholarly journals Sharp inequalities of Kolmogorov type for non-periodic functions on the real domain

2015 ◽  
Vol 23 ◽  
pp. 3
Author(s):  
T.R. Bіkkuzhyna ◽  
V.A. Kofanov
Keyword(s):  
Periodic Functions ◽  
Kolmogorov Type ◽  
The Real ◽  
Extremum Problems ◽  
Real Domain

We obtained sharp inequalities of Kolmogorov type for non-periodic functions on the real domain. The obtained results were applied to solve some extremum problems for non-periodic functions and splines on the real domain.

scholarly journals On inequalities of Kolmogorov type for fractional derivatives of functions defined on the real domain

2021 ◽  
Vol 16 ◽  
pp. 28
Author(s):  
V.F. Babenko ◽  
M.S. Churilova
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Kolmogorov Type ◽  
The Real ◽  
Higher Derivative ◽  
Real Domain ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
New Inequalities

We obtain new inequalities that generalize known result of Geisberg, which was obtained for fractional Marchaud derivatives, to the case of higher derivatives, at that the fractional derivative is a Riesz one. The inequality with second higher derivative is sharp.

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

Linear Differential Equations in the Real Domain

1967 ◽  
Vol 51 (378) ◽  
pp. 364
Author(s):  
R. P. Gillespie ◽  
Kenneth S. Miller
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
The Real ◽  
Real Domain ◽  
Linear Differential

On certain expansions of the solutions of the general Lamé equation

1942 ◽  
Vol 38 (4) ◽  
pp. 364-367 ◽  
Author(s):  
A. Erdélyi
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Recurrence Relations ◽  
Characteristic Exponent ◽  
Periodic Functions ◽  
The Real ◽  
Lamé Equation ◽  
Arbitrary Complex ◽  
Principal Value ◽  
Image Position

1. In this paper I shall deal with the solutions of the Lamé equationwhen n and h are arbitrary complex or real parameters and k is any number in the complex plane cut along the real axis from 1 to ∞ and from −1 to −∞. Since the coefficients of (1) are periodic functions of am(x, k), we conclude ](5), § 19·4] that there is a solution of (1), y0(x), which has a trigonometric expansion of the formwhere θ is a certain constant, the characteristic exponent, which depends on h, k and n. Unless θ is an integer, y0(x) and y0(−x) are two distinct solutions of the Lamé equation.It is easy to obtain the system of recurrence relationsfor the coefficients cr. θ is determined, mod 1, by the condition that this system of recurrence relations should have a solution {cr} for whichk′ being the principal value of (1−k2)½

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