IUMPA

Our work consists of applying the techniques from functional analysis to the rigorous solution of mathematical problems in engineering, by modelling them through ordinary differential equations and partial differential equations, and by the analysis of their solutions and the mathematical properties they possess.

We are concerned with specific problems on the relationship between topology and the functional analysis, for certain kinds of locally convex spaces, including spaces of Fréchet, their topological duals, spaces of continuous functions C(X) and the spaces of distributions and analytical functions. We study topological invariants, such as tightness, Lindelof, Souslin and Hewitt numbers with applications to the topological characterization of properties of concrete objects of functional analysis, to obtain new characterizations, applications and better understanding of certain properties. Combinative techniques of descriptive topology of sets as K-analiticity, analiticity, almost-Souslin, semicontinuity, etc with techniques of local convexity. This topics are in part developed in the monograph “Descriptive Topology in Selected Topics of Functional Analysis”, Developments in Mathematics 24, Springer 2011

Topological vector spaces.

Barrlledness and applications vector spaces with and without local convexity conditions and properties of strong and weak barrelledness. Countably additive vector measures, location properties and Banach spaces including spaces $L_p$ are also studied as well as the wavelets in solving differential models.

Integration of new technologies to the Mathematics education.

The different aspects that involve the use of new technologies, including the use of mathematical programs and educational platforms are studied.

 

Head of the Group	e-mail
Peris Manguillot, Alfred	aperis@mat.upv.es
Researchers
Barrachina Civera, Xavier	xabarci@doctor.upv.es
Conejero Casares, Alberto	aconejero@mat.upv.es
Martínez Jiménez, Félix	fmartinez@mat.upv.es
Murillo Arcila, Marina	mamuar1@posgrado.upv.es
Puig de Dios, Yunied	yupuide@posgrado.upv.es
Ródenas Escribà, Francisco	frodenas@mat.upv.es
PhD Students
Aroza Benlloch, Javier	jaarben@upvnet.upv.es
Bartoll Arnau, Salud	sbartoll@mat.upv.es
Galán, Víctor
Jiménez Munguía, Ronald
Nogués Martínez, Rafael	ranomar@posgrado.upv.es

 

Head of the Group	e-mail
Fernández de Córdoba Castellá, Pedro José	pfernandez@mat.upv.es
Researchers
Abraham Ibrahim, Sergio	sabraham@mat.upv.es
Fuente Herraiz, David	dafueher@upv.es
Giménez Palomares, Fernando	fgimenez@mat.upv.es
Hoyas Calvo, Sergio	sergio.hoyas@mot.upv.es
Isidro San Juan, José María	joissan@mat.upv.es
Martínez Molada, Eulalia	eumarti@mat.upv.es
Pérez Quiles, María Jezabel	jperezq@mat.upv.es
Sanchis Llopis, José María	jmsanchis@mat.upv.es
Siurana paula, María	masiupau@upv.es
Soler Fernández, David	dsoler@mat.upv.es
Urchueguía Schölzel,Javier Fermín	jfurchueguia@fis.upv.es

    Research Lines: Mathematical models, Numerical methods,  Photonics, Synthetic Biology.

Our main research area is the study of methods of functional analysis and their applications to several areas of mathematical analysis, like complex analysis, operator theory, Fourier analysis, dynamical systems and linear partial differential operators.

More precisely, we work in the following problems:

(1) Spaces of analytic functions and operators between them: weighted spaces of analytic functions, composition, superposition and Toeplitz operators, operators on spaces of real analytic functions.

(2) Localization operators and time-frequency analysis: Stockwell transform, uncertainty principles, weighted modulation spaces, frames for Fréchet spaces.

(3) Linear partial differential and convolution operators on spaces of ultradifferentiable functions and ultradistributions: solution operators, hypoellipticity, iterates of the operator, quasianalytic classes, extension of smooth functions, and

(4) Abstract functional analytic developments: splitting of short exact sequences, mean ergodic operators, topological algebras and linear dynamical systems.

 

Head of the Group	e-mail
Bonet Solves, José	jbonet@mat.upv.es
Researchers
Gómez Collado, María del Carme	mcgomez@mat.upv.es
Jorda Mora, Enrique	ejorda@mat.upv.es
Jornet Casanova, David	djornet@mat.upv.es
PhD Students
Beltrán Meneu, María José	mabelme@csa.upv.es
Castillo Medina, Jaime	jaicasme@upvnet.upv.es
Primo Tárraga, Eva	atirpe.23@gmail.com

 

External Collaborators	University
Albanese, Ángela	Università del Salento
Domański, Pawel	Adam Mickiewicz University
Fernández Rosell, Carmen	Universitat de València
Frerick, Leonhard	Universität Trier
Galbis Verdú, Antonio	Universitat de València
Ribera Puchades, Juan Miguel	Universitat de València

The research topics of our group focus on the study of the singularities of real and complex maps, both from the algebraic and the differential point of view. Therefore, our research topics include current problems of algebraic geometry, commutative algebra and differential geometry. We also consider the applications of singularity theory to other fields, like the theory of error correcting codes.