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Comparing Norms of Polynomials in One and Several Variables

✍ Scribed by Igor E. Pritsker

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
194 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

We study Nikolskii-type inequalities for the L norms of an algebraic polynop mial in one variable, defined either by a contour integral or by an area integral over a Jordan domain in ‫.ރ‬ Further, we generalize the one-dimensional results to the case of polynomials in several variables over product domains in ‫ރ‬ m , m ) 1.

πŸ“œ SIMILAR VOLUMES

Products of Many-Variable Polynomials: P
Products of Many-Variable Polynomials: Pairs That Are Maximal in Bombieriβ€²s Norm
✍ B. Beauzamy πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 315 KB

We continue the research initiated in Beauzamy et al. (J. Number Theory 36 (1990), 219-245) and Beauzamy et al. (to appear) about products of many-variable polynomials. We investigate the pairs \((P, Q)\) which are maximal for products in Bombieri's norm (that is for which \([P Q]\) is a large as po

On a Lower-Bound for the Absolute Value
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✍ B. Paneah πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 268 KB

For an arbitrary polynomial \(P\left(z_{1}, z_{2}, \ldots, z_{n}\right)\) in complex space \(\mathbb{C}^{n}\) we describe a set of nonnegative multi-indices \(\alpha=\left(\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}\right)\) such that for any \(n\)-tuple \(\delta=\left(\delta_{1}, \delta_{2}, \ldots,