Derivatives of the L-cosine transform

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

     

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

     

Concentration of mass on the Schatten classes

Let 1?p?∞ and be the unit ball of the Schatten trace class of matrices on Cn or on Rn, normalized to have Lebesgue measure equal to one. We prove that

     

On a factorization of homeomorphisms of the circle possessing periodic points

We prove that for every orientation-preserving homeomorphism possessing periodic points of order n there exist a homeomorphism such that Tn=id and a homeomorphism without periodic points except fixed points such that

F=Tq○G     

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

     

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

     

Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN:

     

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)

     

Duality techniques for certain integral transforms to be starlike

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

     

Relaxation and regularity in the calculus of variations

In this work we prove that, if L(t,u,ξ) is a continuous function in t and u, Borel measurable in ξ, with bounded non-convex pieces in ξ, then any absolutely continuous solution to the variational problem

     

Spectral estimates of least energy solutions to the Brezis-Nirenberg problem with a variable coefficient

Let uε be a least energy solution to the Brezis-Nirenberg problem: