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- Title
Estimates of the distances to direct lines and rays from the poles of simplest fractions bounded in the norm of L <sub> p </sub> on these sets.
- Authors
Borodin, P.
- Abstract
For each p > 1, we obtain a lower bound for the distances to the real axis from the poles of simplest fractions (i.e., logarithmic derivatives of polynomials) bounded by 1 in the norm of L p on this axis; this estimate improves the first estimate of such kind derived by Danchenko in 1994. For p = 2, the estimate turns out to be sharp. Similar estimates are obtained for the distances from the poles of simplest fractions to the vertices of angles and rays.
- Subjects
FRACTIONS; RATIONAL numbers; POLYNOMIALS; LOGARITHMS; RAYS (Graph theory); ANGLES
- Publication
Mathematical Notes, 2007, Vol 82, Issue 5/6, p725
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434607110168