Acta Mathematica Hungarica
Volume/Issue:
Volume 126: Issue 1-2
Complex measures having quadrature formulae with optimal exactness
Authors:
E. Berriochoa Universidad de Vigo Facultad de Ciencias 32004 Ourense Spain

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A. Cachafeiro Universidad de Vigo E.T.S. Ingenieros Industriales 36310 Vigo Spain

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J. García-Amor Universidad de Vigo E.T.S. Ingenieros Industriales 36310 Vigo Spain

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Pages:
51–64
Online Publication Date:
06 Nov 2009
Publication Date:
01 Jan 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-009-8236-5
Keywords:
Gaussian quadrature formula; Szegő quadrature formula; m-point quadrature formula; orthogonal polynomial; support of the measure; 33C47; 42C05; 65D32
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Abstract  

We characterize the supports of the measures having quadrature formulae with similar exactness as Gauss’ theorem. Indeed we obtain the supports of the measures from which an m-point quadrature formula can be obtained such that it exactly integrates functions in the space ℙm−k,m−k[
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\bar z$$ \end{document}
, z]. We also give a method for obtaining the nodes and the quadrature coefficients in all the cases and, as a consequence, we solve the same problem in the space of trigonometric polynomials.
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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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