Some Fourier-type operators for functions on unbounded intervals (Q624249)

In order to approximate functions defined on the real axis or on the real semiaxis, the authors construct and study a new polynomial operator of Fourier type which is the continuous version of a Lagrange-type projector introduced and studied by the same authors in [Math. Comp. 79, No.~269, 327--352 (2010; Zbl 1196.41004)] In particular, they prove necessary and sufficient conditions for the boundedness of these operators in suitable weighted \(L^p\) spaces \((1<p<+\infty)\) and give error estimates in weighted \(L^p\) and in uniform norms.