The problem to be studied goes back to a question of Erdös and Kövari, concerning functions \(M(x), x \in R_{0}{ }^{+}\), which are positive and logarithmically convex in \(\ln x\). The question to find necessary and sufficient conditions for the existence of a power series \[ N(x)=\sum c_{n} x^{n}
On the Approximation of Positive Functions by Power Series, II
✍ Scribed by Ulrich Schmid
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 242 KB
- Volume
- 92
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
We consider positive functions h=h(x) defined for x # R + 0 . Conditions for the existence of a power series N(x)= c n x n , c n 0, with the property
x 0, for some constants d 1 , d 2 # R + , are investigated in [J. Clunie and T. Ko vari,
📜 SIMILAR VOLUMES
## Abstract The degree of pointwise approximation in the strong sense of 2π‐periodic functions from __L^p^__ (__p__ = (1 + α)^−1^, α > −1/2) is examined. An answer to the modified version of Leindler's problem [4] is given.
Research in approximation theory in Russia dates back to P. L. Chebyshev's memoir ``The orie des me canismes connus sous le nom de paralle logrammes'' (Me m. Pre s. Acad. Imp. Sci. Pe tersb. Divers Savants, 1854, VII, 539 568). This memoir posed the problem of the best approximation of functions by
The paper studies the degree of approximation of functions associated with Hardy᎐Littlewood series in the Holder metric.