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 nat...

The hydrodynamic limit of a kinetic Cucker-Smale flocking model is investigated. The starting point is the model considered in [17], which in addition to free-transport of individuals and a standard Cucker-Smale alignment operator, includes Brownian noise and strong local alignment. The latter was derived in [18] as the singular limit of an alignment operator first introduced by Motsch and Tadm...

The standard (point-wise) linear channel model for MIMO wireless systems provides a simplistic mapping from antenna elements to continuous (operator) view point of wireless channels. Low-rank, high-dimension sampling matrices generated by Ray-Tracing may be used to estimate (with error) the “true” operator channel. In order to achieve reasonable estimation error bounds, intractably large dimens...

Point interactions for the second derivative operator in one dimension are studied. Every operator from this family is described by the boundary conditions which include a 2×2 real matrix with the unit determinant and a phase. The role of the phase parameter leading to unitary equivalent operators is discussed in the present paper. In particular it is shown that the phase parameter is not redun...