An explicit method is derived for collocating either of the convolution integrals p(x) = fi f(x t)g(t)dt or q(x) = /*/(< x)g(t)dt, where x 6 (a, b), a subinterval of M . The collocation formulas take the form p = F(Am)% or q = F(Bm)g, where g is an w-vector of values of the function g evaluated at the "Sine points", Am and Bm are explicitly described square matrices of order m, and F(s) = ¡Qexp...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically free with amalgamation over a subalgebra. Therefore we can define a “rectangular free convolution”, linearized by cumulants and by an analytic integral...

Abstract Working in the frame of variable bounded variation spaces sense Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence means classical convolution integral operators. In proposed approach, a crucial step is modulus smoothness for absolutely continuous functions. Several preliminary properties $$p(\cdot )$$ <...