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Polynomials with laguerre weights in Lp

  • H. N. Mhaskar
  • E. B. Saff
Orthogonal Polynomials
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

For each p (0 < p ≤ ∞), s ≥ 0, and integer m ≥ 1 we consider the extremal problem
$$E_{s,m,p} : = \inf \left\{ {\left\| {t^s e^{ - t} \left( {t^m - q_{m - 1} \left( t \right)} \right)} \right\|_L p:q_{m - 1} \in p_{m - 1} } \right\},$$
where the Lp-norm is taken over [0, ∞) and pm−1 is the collection of polynomials of degree at most m−1. The asymptotic behavior of Es,m,p as n:=s+m → ∞ and s/n → ϑ is determined along with the zero distribution for the associated Chebyshev polynomials. The paper includes the proofs of results announced in [7].

Keywords

Extremal Problem Laguerre Polynomial Exponential Weight Haar System Lebesgue Measurable Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • H. N. Mhaskar
    • 1
  • E. B. Saff
    • 2
  1. 1.Department of MathematicsCalifornia State UniversityLos Angeles
  2. 2.Department of MathematicsUniversity of South FloridaTampa

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