Shape-Preserving Approximation by Real Multivariate Polynomials

Extending the results in the univariate case, in this chapter we prove approximation results preserving multivariate shapes, by Bernstein-type, convolutiontype, and tensor-product-type polynomials. The multivariate shapes considered are Popoviciu convexity, Schur convexity, axial convexity, polyhedral convexity, usual multivariate convexity, subharmonicity, and in general, L-convexity, with L a bounded linear operator satisfying some suitable conditions.


Univariate Case Bernstein Polynomial Polyhedral Convexity Bivariate Case Bibliographical Note 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2008

Personalised recommendations