Functional analysis and partial differential equations are two related areas of mathematics which have become crucial for the development of mathematical analysis since the beginning of the last century. The purpose of functional analysis is the study of classes of functions and operators defined between them with the objective of solving problems coming, not only from mathematical analysis, but also from many other areas, such as approximation theory, ergodic theory, numerical analysis, control theory, economical analysis, quantum theory, dynamical systems, harmonic analysis, or partial differential equations.

The theory of partial differential equations plays a central role in pure and applied mathematics, and its study has provided and continues to provide results of enormous theoretical and practical interest. In particular, we are interested in microlocal analysis, pseudodifferential operators, Cauchy problems, dynamical behaviour of their solutions, regularity, etc.
Moreover, in this special session we also want to represent a sample of other topics related to or depending directly on functional analysis, such as Banach space theory, C₀-semigroups of operators, and hypercyclicity, among others.

In Spain, functional analysis is an area with a long tradition as shown by the large number of researchers working on it and its applications that keep it fairly active. On the other hand, Italy is a country with several groups investigating actively in partial differential equations. That is the reason why both countries host a large contingent of young researchers, with varying degrees of maturity, and who represent the future of these areas in Italy and Spain.

Our main objective is to give visibility, at least at a national level, to Italian and Spanish young researchers in functional analysis and partial differential equations and, to enhance contact and communication between them for future collaborations.

• Chiara Boiti (University of Ferrara, Italy)
• J. Alberto Conejero Casares (Polytechnic University of Valencia, Spain)
• David Jornet Casanova (Polytechnic University of Valencia, Spain) - djornet@mat.upv.es

Below you can download the schedule and the abstracts of all talks of this special session.

• Alessia Ascanelli (University of Ferrara, Italy)

          Necessary and sufficient conditions for well-posedness of p-evolution equations with time and space depending coefficients

• María José Beltrán Meneu (University of Valencia, Spain)

          Classical operators on the Hörmander algebras

• José Manuel Calabuig Rodríguez (Polytechnic University of Valencia, Spain)

           Smoothness  on L^p of a vector measure

• María del Carmen Gómez Collado (Polytechnic University of Valencia, Spain)

           Fredholm weighted composition operators on weighted Banach spaces of analytic functions

• Antonio J. Guirao Sánchez (Polytechnic University of Valencia, Spain)

           Preserved extreme points and Morris norms

• Enrique Jordá Mora (Polytechnic University of Valencia, Spain)

           Smoothness of the norm in Banach spaces of vector-valued functions

• Thomas Kalmes (Chemnitz University of Technology, Germany)

           Surjectivity of augmented linear partial differential operators

• Pedro J. Miana (University of Zaragoza, Spain)

          Orthogonal expansions for families of operators

• Michele Miranda (University of Ferrara, Italy)

           Perimeters and short-time behaviour of the heat semigroup

• Alessandro Morando (University of Brescia, Italy)

          Well-posedness of the linearized problem for MHD contact discontinuities in 2D

• Alessandro Oliaro (University of Turin, Italy)

          Global regularity of twisted differential operators

• Natalia Romero (University of La Rioja, Spain)

          Quadrature formulas for orthogonal polynomials

• Pablo Sevilla Peris (Polytechnic University of Valencia, Spain)

          Convergence of Dirichlet and power series

• André Suess (University of Barcelona, Spain)

           Random-field solutions to linear hyperbolic stochastic partial differential equations with variable coefficients

• Pedro Tradacete Pérez (Charles III University of Madrid, Spain)

           Optimal rearrangement invariant range for Hardy type operators

• Sven-Ake Wegner (University of Wuppertal, Germany)

          Growth bound and spectral bound for semigroups on Fréchet spaces