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Muntz's Theorem on compact subsets of positive measure
| Content Provider | Semantic Scholar |
|---|---|
| Author | Borwein, Peter Erdélyi, Tamás |
| Copyright Year | 1995 |
| Abstract | The principal result of this paper is a Remez-type inequality for M\"untz polynomials: $$p(x) := \sum^n_{i=0} a_i x^{\lambda_i}, $$ or equivalently for Dirichlet sums: $$P(t) := \sum^n_{i=0}a_i e^{-\lambda_i t},$$ where $(\lambda_i)_{i=0}^{\infty}$ is a sequence of distinct real numbers. The most useful form of this inequality states that for every sequence $(\lambda_i)^\infty_{i=0}$ satisfying $$\sum^\infty_{\scriptstyle{i = 0} \atop \scriptstyle{\lambda_i \neq 0}}\frac{1}{|\lambda_i|} 0$, remain valid with $[a,b]$ replaced by an arbitrary compact set $A \subset (0,\infty)$ of positive Lebesgue measure. This extends earlier results of the authors under the assumption that the numbers $\lambda_i$ are nonnegative. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.tamu.edu/~terdelyi/papers-online/compact.pdf |
| Alternate Webpage(s) | http://www.cecm.sfu.ca/ftp/pub/CECM/Preprints/Postscript/95:045-Borwein.ps.gz |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
