Uniform approximation in the semiring of positive continuous functions
β Scribed by Karel Prikry; Ian Richards
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 396 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0001-8708
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π SIMILAR VOLUMES
The problem to be studied goes back to a question of ErdΓΆs and KΓΆvari, 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}
We consider the distribution of alternation points in best real polynomial approximation of a function f # C[&1, 1]. For entire functions f we look for structural properties of f that will imply asymptotic equidistribution of the corresponding alternation points.
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,