Convergence in Hausdorff Content of Generalized Simultaneous Pade Approximants

Methawee Wajasat, Nattapong Bosuwan

Abstract


Given a vector of the approximated functions analytic on a neighborhood of some compact subset of the complex plane with simply connected complement in the extended complex plane, we prove convergences in Hausdorff content of the corresponding two generalizations of type II Hermite-Pade approximants on some certain sequences. These two generalizations are based on orthogonal and Faber polynomial expansions. As consequences of these convergence results, we give alternate proofs of Montessus de Ballore type theorems for these generalizations.


Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|