Abstract Sharp upper and lower bounds of the Hermitian Toeplitz determinants second third orders are found for various subclasses close-to-convex functions.

This is a survey of our recent joint investigations of lattices that are generated by finite Abelian groups. In the case of cyclic groups, the volume of a fundamental domain of such a lattice is a perturbed Toeplitz determinant with a simple Fisher-Hartwig symbol. For general groups, the situation is more complicated, but it can still be tackled by pure matrix theory. Our main result on the lat...

In this paper we show, how a straightforward and natural application of a pair of fundamental identities valid for polynomials orthogonal over the unit circle, can be used to calculate the determinant of the finite Toeplitz matrix, ∆n = det(wj−k) n−1 j,k=0 := det (

For each natural number m greater than one, and each natural number k less than or equal to m, there exists a root-nding iteration function, deened as the ratio of two determinants that depend on the rst m ? k derivatives of the given function, and for k = 1 are Toeplitz determinants. In this paper we analyze the order of convergence of this fundamental family. For xed m, as k increases, the or...

In this paper, we obtain the upper bounds of Toeplitz determinants for class functions with bounded turning. We also present some consequences our main results. Some estimates obtained on are sharp.

Sharp upper and lower bounds for the second third order Hermitian–Toeplitz determinants are obtained some general subclasses of starlike convex functions. Applications these results also discussed several widely known classes.

This is a survey of Harold Widom’s work in Toeplitz operators, embracing his early results on the invertibility and spectral theory investigations eigenvalue distribution convolution groundbreaking research into Wiener–Hopf determinants.

Sharp lower and upper bounds of the second- third-order Hermitian Toeplitz determinants for class α-convex functions were found. The symmetry properties arithmetic mean underlying definition α-convexity matrices used.

In this paper, we are introducing certain subfamilies of holomorphic functions and making an attempt to obtain upper bound (UB) the second third order Hankel determinants by applying lemmas, Toeplitz determinants, for normalized analytic belong these classes, defined on open unit disc in complex plane. For one inequality, have obtained sharp bound.