Volume 30, Issue 2
A Remark on Pál Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle

Anal. Theory Appl., 30 (2014), pp. 173-192.

Published online: 2014-06

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• Abstract

In this paper we study the problem of explicit representation and convergence of Pál type (0;1) interpolation and its converse, with some additional conditions, on the non-uniformly distributed nodes on the unit circle obtained by projecting the interlaced zeros of $P_n(x)$ and $P′_n(x)$ on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and Pál type interpolations on non-uniformly distributed zeros on the unit circle.

• Keywords

Pál type interpolation, non-uniformly distributed set of points on unit circle, Legendre polynomials.

41A05, 41A10, 41A25

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@Article{ATA-30-173, author = {}, title = {A Remark on Pál Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {2}, pages = {173--192}, abstract = {

In this paper we study the problem of explicit representation and convergence of Pál type (0;1) interpolation and its converse, with some additional conditions, on the non-uniformly distributed nodes on the unit circle obtained by projecting the interlaced zeros of $P_n(x)$ and $P′_n(x)$ on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and Pál type interpolations on non-uniformly distributed zeros on the unit circle.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n2.4}, url = {http://global-sci.org/intro/article_detail/ata/4483.html} }
TY - JOUR T1 - A Remark on Pál Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle JO - Analysis in Theory and Applications VL - 2 SP - 173 EP - 192 PY - 2014 DA - 2014/06 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n2.4 UR - https://global-sci.org/intro/article_detail/ata/4483.html KW - Pál type interpolation, non-uniformly distributed set of points on unit circle, Legendre polynomials. AB -

In this paper we study the problem of explicit representation and convergence of Pál type (0;1) interpolation and its converse, with some additional conditions, on the non-uniformly distributed nodes on the unit circle obtained by projecting the interlaced zeros of $P_n(x)$ and $P′_n(x)$ on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and Pál type interpolations on non-uniformly distributed zeros on the unit circle.

N. Mathur & P. Mathur. (1970). A Remark on Pál Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle. Analysis in Theory and Applications. 30 (2). 173-192. doi:10.4208/ata.2014.v30.n2.4
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