Duality techniques for certain integral transforms to be starlike

For β<1, let denote the class of all normalized analytic functions f such that

     

Some functional inverse Santaló inequalities

Let be a log-concave function and for z∈Rn, define

     

Derivatives of the L-cosine transform

The L^p-cosine transform of an even, continuous function is defined by

     

Complete decomposition of Dickson-type polynomials and related Diophantine equations

We characterize decomposition over C of polynomials defined by the generalized Dickson-type recursive relation (n?1)

     

Second-order energies on thin structures: variational theory and non-local effects

For a given positive measure μ on , we consider integral functionals of the kind

     

On multicolour noncomplete Ramsey graphs of star graphs

Given graphs , where k≥2, the notation

     

The solution manifold and C-smoothness for differential equations with state-dependent delay

Let h>0, open, and continuously differentiable. If f satisfies two mild additional smoothness conditions then the set

     

On the numerical radius of operators in Lebesgue spaces

We show that the absolute numerical index of the space Lp(μ) is (where ). In other words, we prove that

     

Global branch from the second eigenvalue for a semilinear Neumann problem in a ball

Let (n?3) be a ball, and let f∈C³. We are concerned with the Neumann problem

     

Regularity for a fourth-order critical equation with gradient nonlinearity

Given Ω a smooth bounded domain of Rn, n?3, we consider functions that are weak solutions to the equation

     

Simultaneous Diophantine approximation on manifolds and Hausdorff dimension

Let M be an m-dimensional, C^k manifold in , for any , and for any τ>0 let

     

The left-definite spectral theory for the Dunkl-Hermite differential-difference equation

In this paper, we develop the left-definite spectral theory associated with the self-adjoint operator A_μ in , generated from the Dunkl second-order Hermite differential equation

     

Norm estimates of almost Mathieu operators

We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C^*-algebra . In the process, we prove for every λ∈R and the inequality