Abstract Stenger conjectures are claims about the location of eigenvalues matrices whose elements certain integrals involving basic Lagrange interpolating polynomials supported on zeros orthogonal polynomials. In this paper, we show validity extended conjecture for families classical We also restricted Strenger a family Jacobi and generalized Laguerre A connection with -stability collocation Ru...

We use the method of interlacing families polynomials to derive a simple proof Bourgain and Tzafriri’s Restricted Invertibility Principle, then sharpen result in two ways. show that stable rank can be replaced by Schatten 4-norm tighter bounds hold when number columns matrix under consideration does not greatly exceed its rows. Our are derived from an analysis smallest zeros Jacobi associated L...

We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also correspo...

It is proved that a polynomial p of the form