ACTIVITIES

- To promote the collaboration between the distinct groups which compose the network.

- To encourage relations with other research groups in these topics.

- To facilitate the mobility of the researchers of the network.

- To think about the new perspectives of research in our area.

- To convert this web site into a useful tool for research in Complex Analysis and Operator Theory as well as a meeting point for researchers working on these fields or any other related topics.

- To organize meetings (workshops, winter/summer schools, conferences,...) on our research topics.

This Network is currently composed by approximately 90 researchers, most of them spreaded out in 20 Spanish universities whose main areas of research are Complex Analysis and Operator Theory.

Since the year 2004, the Network exists as an official entity financed by the Scientific Department of the Spanish govermment. Since 2004 to 2015, the general coordinator of this network was Daniel Girela (Universidad de Málaga) and since 2015 this role has been taken over by José Ángel Peláez (Universidad de Málaga). It is supported by the steering-scientific committee of the network.

Complex Analysis and Operator Theory are two of the most classical branches of mathematical analysis and they are very closely related, as being often the source of many important results. Furthermore, these two branches have close links with others, such as Harmonic Analysis, Probability Theory, Functional Analysis and Geometry. The interplay between all these branches gives rise to very beautiful results and makes our area of research so interesting and live.

This network has been created with the aim of improving the quality and the diffusion of Complex analysis and Operator Theory. More precisely, we intent:

- Classical theory of spaces of analytic functions: Interpolation and sampling. Factorization. Properties of integrability of the derivatives of inner functions. Embedding theorems between spaces of analytic functions.
- Operators between spaces of analytic functions: Toeplitz operators in Hardy and Bergman spaces. Composition operators. Superposition operators. Integration operators. Multipliers...
- Other function spaces: Spaces of vector valued analytic functions. Spaces of real and quasi-analytic functions. Spaces of ultradifferentiable functions.
- Geometric function theory: General theory of conformal mappings. Properties of integrability of the derivatives of univalent functions. Conformal mappings and function spaces. Planar domains as images of the disc under conformal mappings. Angular derivative. Boundary behaviour of analytic functions. Hyperbolic geometry. Extremal problems. Harmonic mappings in the plane, Schwarzian derivatives. Value distribution theory.
- Riemann surfaces, Gromov hyperbolicity: Classification theorems for Riemann surfaces. Gromov hyperbolicity in metric spaces and, in particular, in Riemann surfaces. Harmonic functions in graphs.
- Approximation theory: Problems of simultaneous approximation by polynomials in spaces of analytic functions. Questions of polynomial approximation and completeness in weighted Sobolev spaces.
- Dynamical systems: Study of the processes generated by the iteration of an analytic function. Semigroups of holomorphic functions. Semigroups of composition operators. Hypercyclicity, supercyclicity, mixing.
- Geometry of Banach spaces: Fixed point theory. Differential equations and difference equations in Banach spaces.

- Theory of weights: Majorants, Hardy-Littlewood (Hörmander) maximal functions, non-tangential maximal functions, weighted projections, two-weight inequality for the Hilbert transform,...

The main lines of research pursued by the distinct groups which compose the network are the following:

17.6.2019 - 20.6.2019

ACOTCA. Advanced Courses in Operator Theory and Complex Analysis.

Paris. France.

25.06.2019 - 28.06.2019

Barcelona Analysis Conference.

Barcelona. España.

1.9.2019 - 30.11.2019

Geometry and analysis in function and mapping theory on Euclidean and metric measure spaces.

Warsaw. Poland.

WORKSHOP AND MEETING ORGANIZED BY THE NETWORK

13.5.2019 - 16.5.2019

Fifth Summer School in Complex Analysis and Operator theory.

Cullera. Valencia. España.

26.05.2018 - 30.05.2018

Spaces of functions and operators between them. Blanes (Gerona). Spain.

SPANISH NETWORK IN COMPLEX ANALYSIS AND OPERATOR THEORY