Let Λ be a set of three integers and let CΛ be the space of 2π-periodic functions with spectrum in Λ endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T ∈ CΛ and prove that x is unique unless |T | has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of CΛ, to describe how the maximum modulus...

In this paper we impose distinct restrictions on the moduli of zeros p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate dependence ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 MαMα Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| certain coefficients p(z)p(z). This comprises several results, which in particular yields some classical polynomial inequalities as special cas...

In this paper we consider subharmonic functions »gl in the unit disk whose minimum modulus and maximum modulus satisfy a certain inequality. We show the existence of an extremal member of this class with largest maximum modulus. We then obtain an upper bound for the maximum modulus of this function in terms of the logarithmic measure of a certain set. We use this upper bound to prove theorems a...

We study, for the first time, maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point each modulus. Blumenthal showed entire maps either whole plane, or countable union analytic curves. show in case, by way contrast, any closed containing can be attained as These examples all polynomial type. also that, subject an addit...

seismic piezocone device (scptu) together with resonant column and cyclic triaxial test apparatus are employed to measure small strain shear modulus (g0) of carbonate sandy and clayey soils of southern coasts of iran. a large area of southern regions of iran is formed from clay, silt and sand. in this study, maximum shear modulus that is derived from both field (by seismic piezocone) and labora...