Author | Totik, Vilmos. author |
---|---|

Title | Weighted Approximation with Varying Weight [electronic resource] / by Vilmos Totik |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1994 |

Connect to | http://dx.doi.org/10.1007/BFb0076133 |

Descript | VI, 118 p. online resource |

SUMMARY

A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained

CONTENT

Freud weights -- Approximation with general weights -- Varying weights -- Applications

Mathematics
Potential theory (Mathematics)
Functions of real variables
Mathematics
Real Functions
Potential Theory