Some properties of sinc-approximations of continuous functions on a segment are studied. For the first time, the sinc-approximations arose in the work of Pleynet. Later, in connection with developments in signals coding theory, E. Borel and E. T. Whittaker introduced the notions of a cardinal function and a truncated cardinal function, the restriction of which to [0, π] looks like this:

Orbit functions of a simple Lie group/Lie algebra L consist of exponential functions summed up over the Weyl group of L. They are labeled by the highest weights of irreducible finite dimensional representations of L. They are of three types: C-, Sand E-functions. Orbit functions of the Lie algebras An, or equivalently, of the Lie group SU(n+1), are considered. First, orbit functions in two diff...

We show that, given a histogram with n bins—possibly non-contiguous or consisting of single points—there exists a unique polynomial histopolant (polynomial of order n with bin averages equal to the histogram’s). We also present histopolating cardinal functions for histograms with contiguous bins. The Hodge star operator from the theory of differential forms is the mapping which puts kand (d − k...

The solutions provided in this work address the classic but still relevant topic of establishing new classes univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects quantum calculus are also considered research make it more unique produce pleasing outcomes. We introduce connected polynomials, which generalize certain previously investigated ...