𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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


On the Approximation of Positive Functio
✍ U. Schmid 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 124 KB

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 Strong Approximation by (C, α)-Me
✍ Włodzimierz Łenski 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 430 KB

## 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.

On the Article by V. L. Goncharov, “The
✍ Vladimir M. Tikhomirov 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 98 KB

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