Let C be a non-degenerate planar curve. We show that the curve is of Khintchine-type for convergence in the case of simultaneous approximation in R 2 with two independent approximation functions; that is if a certain sum converges then the set of all points (x, y) on the curve which satisfy simultaneously the inequalities qx < ψ1(q) and qy < ψ2(q) infinitely often has induced measure 0. This co...

A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they...

We study the simultaneous approximation properties of the Bézier variant of the well known Phillips operators and estimate the rate of convergence of the Phillips-Bézier operators in simultaneous approximation, for functions of bounded variation.

In a recent paper, Kim and Nakada proved an analogue of Kurzweil’s theorem for inhomogeneous Diophantine approximation of formal Laurent series over finite fields. Their proof used continued fraction theory and thus cannot be easily extended to simultaneous Diophantine approximation. In this note, we give another proof which works for simultaneous Diophantine approximation as well.

In a seminal paper Nagar (1959) obtained moment approximations for the k-class of estimators in a general static simultaneous equation model under the assumption that the structural disturbances were i.i.d and normally distributed. While it has been known for some time that the normality assumption can be relaxed when obtaining the bias approximation, it has not been demonstrated that the secon...