Suppose ß is a bounded, strongly convex domain in C^ with smooth boundary and <p\ £2 —» Í2 is an arbitrary holomorphic map. While in general the composition operator C^ need not map the Hardy space… (More)

We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.

We develop Trapezoid, Midpoint, and Simpson’s rules for the Riemann-Stieltjes integral, the latter two being new. These rules are completely natural when the notion of relative convexity is used.… (More)