CYTUVA

GIR - Applied Functional Analysis (AFA)

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Contact Information

Manuel Núñez Jiménez
Campus Miguel Delibes, Paseo Belén, 7
Valladolid, Valladolid (47011) - Facultad de Ciencias
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983423924
983423013

Basic Information

UniversityUniversidad de Valladolid
Center
DepartmentAlgebra, Mathematical Analysis, Geometry and Topology
Investigation GroupApplied Functional Analysis (AFA)

Description

OBJECTIVES:

The fundamental objective of the GIR AFA is the application of advanced functional analysis techniques to the study of problems within Mathematical Physics, Signal Theory and mathematical theories such as asymptotic developments and dynamic systems. More specifically, the members of the Group have developed their research on the following topics:

Magnetohydrodynamics and Dynamo Theory. Manuel Nuñez Jiménez

Study of the behavior of conductive fluids, including plasmas, light-emitting fluids that constitute the most abundant form of matter in the Universe. Its description is made using mathematical analysis techniques, such as the Maxwell-Boltzmann equations, whose complexity makes it advisable to analyze a simpler model, that of Magnetohydrodynamics, a discipline that studies the dynamics of electrically conductive fluids by combination of Navier-Stokes equations (describe the movement of a fluid) and electromagnetism (describe electromagnetic phenomena).

Among the multiple applications of this theory, the group focuses especially on classical and relativistic astrophysical phenomena, on the growth of the magnetic field (dynamo theory) with its applications to the study of the solar atmosphere, and on the magnetic confinement of plasmas, relevant in the study of controlled nuclear fusion.

Ondículas, ´Frames´ y aplicaciones al Análisis Armónico y la Teoría de la Señal. Félix Galindo Soto y Fernando Gómez Cubillo

La teoría de ondículas (wavelets) es una rama de las Matemáticas que sintetiza ideas del ámbito de la Ingeniería, Física, Análisis Numérico y Matemática Pura, y que constituye una importante herramienta en el procesamiento, análisis e interpretación de señales. Objetivos específicos en esta línea de investigación son el desarrollo de técnicas espectrales y su aplicación en el ámbito de la teoría de la señal, en particular, el procesado de imágenes de resonancia magnética y fondo de ojo orientado al diagnóstico.

Desarrollo asintóticos de funciones de varias variables. Javier Sanz Gil

Se estudia la existencia y el significado analítico de soluciones formales en serie de potencias para diversos tipos de ecuaciones, principalmente diferenciales pero también en q-diferencias-diferenciales o problemas de perturbación singular. Dichas soluciones formales resultan ser representaciones asintóticas de soluciones holomorfas en regiones del plano complejo, que en ocasiones pueden ser reconstruidas mediante procedimientos de sumación. Estas técnicas requieren del estudio de diversos aspectos (transformadas integrales, casianaliticidad, etc.) en el contexto de las clases ultradiferenciables y ultraholomorfas de funciones en una y varias variables, que generalizan las clases clásicas denominadas de Gevrey.

Quantum mechanics. Fernando Gómez Cubillo

Development of functional analysis techniques aimed at studying the mathematical foundations of Quantum Physics. In this line of research, among others, the study of the theory of transformations of Dirac -one of the founders of Quantum Mechanics-, equipment of spectral measurements, Lippmann-Schwinger equations, quantum probability, infinite-dimensional analysis, irreversibility, time operators, etc.

Other information

Number of researchers:

Technological Line(s):

- Experimental sciences

Development status:

In research and development phase

Differentiation in the market:

There are no other suppliers

Applicability of technology:

Yes

Additional Information:

GIR Belonging to IMUVa (Research Institute in mathematics)

UNESCO Code:

1202 - Analysis and functional analysis

Other members:

Félix Galindo Soto
Alberto Lastra Sedano
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Fernando María Gómez Cubillo
Javier Sanz Gil

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