On space maximal curves

Any maximal curve X is equipped with an intrinsic embedding π: X → Pr which reveal outstanding properties of the curve. By dealing with the contact divisors of the curve π(X) and tangent lines, in this paper we investigate the first positive element that the Weierstrass semigroup at rational points can have whenever r = 3 and π(X) is contained in a cubic surface.

On operators with complex Gaussian kernels over Lp spaces

In this paper we study new Lp-boundedness properties and Parseval-type relations concerning the operators with complex Gaussian kernels over the spaces Lp(R,w(x)dx), 1 ? p ? ?, where w represents any function greater than or equal to one almost everywhere on R. Here, the Gauss-Weierstrass semigroup is considered as a particular case of this analysis.

On the Cauchy problem for a generalized nonlinear heat equation

The paper is concerned with the Cauchy problem for a nonlinear generalized heat equation which is related to the generalized Gauss–Weierstrass semigroup via Duhamel’s principle. For the initial data we assume that they belong to some fractional Sobolev spaces. We study the existence and uniqueness of mild and strong solutions which are local in time. Moreover, they are smooth functions and belong to Lebesgue spaces with respect to the space variable. We use both fixed point arguments and mapping properties of the generalized Gauss–Weierstrass semigroup. Finally, we study the well-posedness of the problem.