Approximation of Infinitely Differentiable Functions on the Real Line by Polynomials in Weighted Spaces

2021 ◽  
Author(s):  
I. Kh. Musin
Keyword(s):  
Real Line ◽  
Weighted Spaces ◽  
The Real ◽  
Differentiable Functions ◽  
Infinitely Differentiable Functions

Most Infinitely Differentiable Functions are Nowhere Analytic

1973 ◽  
Vol 16 (4) ◽  
pp. 597-598 ◽  
Author(s):  
R. B. Darst
Keyword(s):  
Open Subset ◽  
Real Numbers ◽  
The Real ◽  
Differentiable Functions ◽  
First Category ◽  
Infinitely Differentiable Functions

We define a natural metric, d, on the space, C∞,, of infinitely differentiable real valued functions defined on an open subset U of the real numbers, R, and show that C∞, is complete with respect to this metric. Then we show that the elements of C∞, which are analytic near at least one point of U comprise a first category subset of C∞,.

scholarly journals Inequalities of various metrics for the norms $$$\|x\|_{p,\delta} = \sup \bigl\{ \| x \|_{L_p[a,b]} \colon a,b\in \mathbb{R}, b-a\leqslant \delta \bigr\}$$$ of differentiable functions on the real domain

2018 ◽  
Vol 26 (1) ◽  
pp. 48
Author(s):  
V.A. Kofanov
Keyword(s):  
Real Line ◽  
Trigonometric Polynomials ◽  
The Real ◽  
Differentiable Functions ◽  
Real Domain

We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differentiable functions defined on the real line, trigonometric polynomials and periodic splines.

scholarly journals Isometries between Spaces of Vector-Valued Differentiable Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Alireza Ranjbar-Motlagh
Keyword(s):  
Banach Space ◽  
Real Line ◽  
Convex Banach Space ◽  
Compact Interval ◽  
The Real ◽  
Strictly Convex ◽  
Differentiable Functions ◽  
Strictly Convex Banach Space ◽  
Vector Valued

This article characterizes the isometries between spaces of all differentiable functions from a compact interval of the real line into a strictly convex Banach space.

scholarly journals On some inequalities in various metrics for differentiable functions on real line

2021 ◽  
Vol 18 ◽  
pp. 123
Author(s):  
V.A. Kofanov
Keyword(s):  
Real Line ◽  
The Real ◽  
Differentiable Functions

We obtain the estimates of the seminorms of Weil of the functions on the real line and their derivatives with the help of local $L_p$-norms of the functions and uniform norms of their highest derivatives.

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