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)

     

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

     

Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity

This paper deals with existence results for the following nonlinear problem with the Dirichlet p-Laplacian Δ_p in a bounded domain :

     

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

     

A min-max theorem for complex symmetric matrices

We optimize the form Re x^tTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,

     

On multicolour noncomplete Ramsey graphs of star graphs

Given graphs , where k≥2, the notation

     

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