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)


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].


Extremal Problem Laguerre Polynomial Exponential Weight Haar System Lebesgue Measurable Function 
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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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