We give a generalisation of the multivariate beta integral. This is used to show that the (multivariate) Bernstein--Durrmeyer operator for a Jacobi weight has a limit as the weight becomes singular. The limit is an operator previously studied by Goodman and Sharma. From the elementary proof given, it follows that this operator inherits many properties of the Bernstein--Durrmeyer operator in a natural way. In particular, we determine its eigenstructure and give a differentiation formula for it. |
Keywords
Math Review Classification
Primary 33B15, 41A10,
; Secondary 15A18, 33C45, 41A36
Last Updated
19 February 2003
Length
10 Pages
Availability
No online versions are available,
but there should be a hardcopy version available from the department.