Instituto de Investigación
en Matemáticas

Análisis Funcional Aplicado

(AFA)


Objetivos: El objetivo fundamental es la aplicación de técnicas avanzadas de Análisis Funcional al estudio de problemas dentro de la Física Matemática, la Teoría de la Señal y teorías matemáticas tales como los desarrollos asintóticos y los sistemas dinámicos. Más específicamente, los miembros del grupo desarrollan sus investigaciones en los siguientes temas: - Magnetohidrodinámica y Teoría Dinamo. Estudio del comportamiento de los fluidos conductores, entre los que se incluyen los plasmas, fluidos emisores de luz que constituyen la forma más abundante de materia en el Universo. Su descripción se realiza mediante el empleo de técnicas de análisis matemático, como las ecuaciones de Maxwell-Boltzmann, cuya complejidad hace aconsejable el análisis de un modelo más sencillo, el de la Magnetohidrodinámica, disciplina que estudia la dinámica de fluidos conductores de electricidad mediante la combinación de ecuaciones de Navier-Stokes (describen el movimiento de un fluido) y de electromagnetismo (describen fenómenos electromagnéticos). Entre las múltiples aplicaciones de esta teoría, el grupo se centra especialmente en fenómenos astrofísicos clásicos y relativistas, en el crecimiento del campo magnético (teoría dinamo) con sus aplicaciones al estudio de la atmósfera solar, y en el confinamiento magnético de plasmas, relevante en el estudio de la fusión nuclear controlada. Investigador principal: Manuel Nuñez Jiménez - Ondículas, 'Frames' y aplicaciones al Análisis Armónico y la Teoría de la Señal. 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. Investigadores principales: Félix Galindo Soto y Fernando Gómez Cubillo - Teoría asintótica de ecuaciones en derivadas parciales y problemas de perturbación singular. 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. Investigador principal: Javier Sanz Gil - Fundamentos matemáticos de la Física Cuántica. Desarrollo de técnicas en Análisis Funcional orientadas al estudio de fundamentos matemáticos de la Física Cuántica. En esta línea de investigación se atiende, entre otros, al estudio de la teoría de transformaciones de Dirac -uno de los fundadores de la Mecánica Cuántica-, equipamientos de medidas espectrales, ecuaciones de Lippmann-Schwinger, probabilidad cuántica, análisis infinito-dimensional, irreversibilidad, operadores de tiempo, etc. Investigador principal: Fernando Gómez Cubillo
Líneas de investigación: Magnetohidrodinámica, Análisis Armónico y Teoría de ondículas, Desarrollos Asintóticos, Mecánica Cuántica
Publicaciones:
Attractors of magnetohydrodynamic flows in an Alfvénic state J. Phys. A 32 5929--5935 (1999) Núñez, Manuel and Sanz, Javier
On strongly asymptotically developable functions and the Borel-Ritt theorem Studia Math. 133 231--248 (1999) Sanz, J. and Galindo, F.
Application of the method of special series in nonlinear mathematical physics Proc. Steklov Inst. Math. 0 S58--S77 (2004) Filimonov, M. Yu.
An improved estimate for the maximal growth order of solutions of linear differential systems Arch. Math. (Basel) 83 256--263 (2004) Pflügel, Eckhard
Asymptotic stability for second-order differential equations with complex coefficients Electron. J. Differential Equations 0 No. 85, 20 pp. (electronic) (2004) Hovhannisyan, Gro R.
Uniform multisummability and convergence of a power series Funkcial. Ekvac. 47 119--127 (2004) Sibuya, Yasutaka
Asymptotic expressions of normalized Laguerre matrix polynomials on bounded intervals Util. Math. 65 3--31 (2004) Jódar, L. and Sastre, J.
Comparison of certain summability methods by speeds of convergence Anal. Math. 29 227--242 (2003) Stadtmüller, Ulrich and Tali, Anne
Linear continuous extension operators for Gevrey classes on polysectors Glasg. Math. J. 45 199--216 (2003) Sanz, J.
Bilinear semiclassical moment functionals and their integral representation J. Approx. Theory 121 71--99 (2003) Bertola, Marco
On a moment problem and a class of perfect summability methods J. Anal. 10 119--123 (2002) Ruscheweyh, Stephan
On the singular behavior of the inverse Laplace transforms of the functions $ rac{I_n(s)}{sI'_n(s)}$ Canad. Math. Bull. 45 399--416 (2002) Iakovlev, Serguei
Asymptotic expansion of two-dimensional Euler-Maclaurin distributional sums Far East J. Math. Sci. (FJMS) 6 1--29 (2002) Ulate, Carlos Ml. and Estrada, Ricardo
Summability in a direction of formal power series in several variables Asymptot. Anal. 29 115--141 (2002) Sanz, Javier
On an integral transform Math. Rep. (Bucur.) 3 353--358 (2002) (2001) Lemnete Ninulescu, Lumini{c{t}}a
Summability of formal power series solutions of ordinary and partial differential equations Funct. Differ. Equ. 8 11--24 (2001) Balser, W.
Multiresolution analysis and Radon measures on a locally compact abelian group Czechoslovak Math. J. 51 859--871 (2001) Galindo, Félix and Sanz, Javier
A generalized moment problem for rapidly decreasing smooth vector functions of several variables J. Math. Anal. Appl. 263 655--665 (2001) Galindo, F. and López, F. and Sanz, J.
Gérard-Sibuya's versus Majima's concept of asymptotic expansion in several variables J. Aust. Math. Soc. 71 21--35 (2001) Hernández, J. A. and Sanz, J.
Constructive Borel-Ritt interpolation results for functions of several variables Asymptot. Anal. 24 167--182 (2000) Hernández, Jesús A. and Sanz, Javier
Uniform growth rates for the magnetic field in a kinematic dynamo J. Phys. A 33 3605--3611 (2000) Núñez, Manuel and Sanz, Javier
Logarithmic order and type of indeterminate moment problems. {II} J. Comput. Appl. Math. 233 808--814 (2009) Pedersen, Henrik L.
Complex moment problems and recursive relations of Fibonacci type Integral Equations Operator Theory 65 307--318 (2009) Ben Taher, Rajae and Rachidi, Mustapha
Carathéodory-Julia type conditions and symmetries of boundary asymptotics for analytic functions on the unit disk Math. Nachr. 282 1513--1536 (2009) Bolotnikov, Vladimir and Kheifets, Alexander
Solution of the polynomial moment problem Proc. Lond. Math. Soc. (3) 99 633--657 (2009) Pakovich, F. and Muzychuk, M.
An approximation property of exponential functions Acta Math. Hungar. 124 155--163 (2009) Jung, S.-M.
Boundary rigidity for some classes of meromorphic functions Oper. Matrices 3 283--301 (2009) Bolotnikov, Vladimir
Stieltjes moment problem in general Gelfand-Shilov spaces Studia Math. 192 111--128 (2009) Lastra, Alberto and Sanz, Javier
The Liouville-Neumann expansion at a regular singular point J. Difference Equ. Appl. 15 119--132 (2009) López, José L.
On complex singularity analysis for linear $-difference-differential equations J. Dyn. Control Syst. 15 83--98 (2009) Malek, Stéphane
Extension operators for the Stieltjes moment problem in classical Gelcprime fand-Shilov spaces Rev. Semin. Iberoam. Mat. 3 65--77 (2008) Lastra, Alberto
Linear versus non-linear acquisition of step-functions J. Geom. Anal. 18 369--399 (2008) Ettinger, B. and Sarig, N. and Yomdin, Y.
Linear continuous operators for the Stieltjes moment problem in Gelfand-Shilov spaces J. Math. Anal. Appl. 340 968--981 (2008) Lastra, Alberto and Sanz, Javier
Calculating the near field of a line of sources using Mellin transforms ANZIAM J. 49 99--109 (2007) Martin, P. A.
Some remarks on $-dimensional Laplace transforms Ital. J. Pure Appl. Math. 0 163--168 (2007) Saberi-Nadjafi, Jafar
Matrix transformations and quasi-Newton methods Int. J. Math. Math. Sci. 0 Art. ID 25704, 17 (2007) Benahmed, Boubakeur and de Malafosse, Bruno and Yassine, Adnan
Universal Taylor series on open subsets of $Bbb R^n$ Analysis (Munich) 26 401--409 (2006) Costakis, G. and Marias, M. and Nestoridis, V.
Cost-reduction in hyperinterpolation Results Math. 49 361--375 (2006) Reimer, Manfred
Basic convergence with rates of smooth Picard singular integral operators J. Comput. Anal. Appl. 8 313--334 (2006) Anastassiou, George A.
Convergence of formal solutions of some nonlinear differential systems at an irregular singularity Asymptot. Anal. 46 93--122 (2006) Rezaoui, Med-Salem
Unique summing of formal power series solutions to advanced and delayed differential equations Discrete Contin. Dyn. Syst. 0 730--737 (2005) Pravica, David W. and Spurr, Michael J.
Growth of solutions of three order differential equations Appl. Math. J. Chinese Univ. Ser. B 20 35--44 (2005) Chen, Zongxuan
Flat functions in Carleman ultraholomorphic classes via proximate orders J. Math. Anal. Appl. 415 623--643 (2014) Sanz, Javier
On Gevrey solutions of threefold singular nonlinear partial differential equations J. Differential Equations 255 3205--3232 (2013) Lastra, Alberto and Malek, Stéphane and Sanz, Javier
Strong asymptotic expansions in a multidirection Funkcial. Ekvac. 55 317--345 (2012) Lastra, Alberto and Mozo-Fernández, Jorge and Sanz, Javier
Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform J. Math. Anal. Appl. 396 724--740 (2012) Lastra, Alberto and Malek, Stéphane and Sanz, Javier
On $q-$asymptotics for linear $q-$difference-differential equations with Fuchsian and irregular singularities J. Differential Equations 252 5185--5216 (2012) Lastra, Alberto and Malek, Stéphane and Sanz, Javier
Power series solutions of singular linear systems Internat. J. Math. 23 1250034, 34 (2012) Han, Jen-Yin and Lin, Chin-Yuan
On $q-$Gevrey asymptotics for singularly perturbed $q-$difference-differential problems with an irregular singularity Abstr. Appl. Anal. 0 Art. ID 860716, 35 (2012) Lastra, Alberto and Malek, Stéphane
On summability of nonlinear mappings: a new approach Math. Z. 270 189--196 (2012) Pellegrino, Daniel and Santos, Joedson
Approximation of extremal solution of non-Fourier moment problem and optimal control for non-homogeneous vibrating systems J. Math. Anal. Appl. 387 241--250 (2012) Sklyar, G. M. and Szkibiel, G.
On the equivalence of singular point quantities and the integrability of a fine critical singular point Nonlinear Anal. Real World Appl. 12 2794--2801 (2011) Zhang, Qi and Liu, Yirong and Chen, Haibo
On approximation of smooth functions from null spaces of optimal linear differential operators with constant coefficients Anal. Theory Appl. 27 187--200 (2011) Vatchev, Vesselin
On adapted coordinate systems Trans. Amer. Math. Soc. 363 2821--2848 (2011) Ikromov, Isroil A. and Müller, Detlef
On higher order boundary derivatives of an analytic self-map of the unit disk J. Approx. Theory 163 568--589 (2011) Bolotnikov, Vladimir
On an interpolation problem for $-Potapov functions Linear Algebra Appl. 434 741--784 (2011) Fritzsche, Bernd and Kirstein, Bernd and Raabe, Uwe
Operational calculus approach to nonlocal Cauchy problems Math. Comput. Sci. 4 243--258 (2010) Dimovski, Ivan and Spiridonova, Margarita
Quasi-analyticity in Carleman ultraholomorphic classes Ann. Inst. Fourier (Grenoble) 60 1629--1648 (2010) Lastra, Alberto and Sanz, Javier
A note on a problem arising from risk theory Czechoslovak Math. J. 60 1049--1053 (2010) Abel, Ulrich and Furdui, Ovidiu and Gavrea, Ioan and Ivan, Mircea
Growth properties of Nevanlinna matrices for rational moment problems J. Approx. Theory 162 2184--2201 (2010) Bultheel, A. and González-Vera, P. and Hendriksen, E. and Nj{aa}stad, O.
Extension operators in Carleman ultraholomorphic classes J. Math. Anal. Appl. 372 287--305 (2010) Lastra, Alberto and Sanz, Javier
On complete interpolating sequences and sampling expansions LMS J. Comput. Math. 13 1--9 (2010) Smith, Kevin
A note on fractional moments for the one-dimensional continuum Anderson model J. Math. Anal. Appl. 365 435--446 (2010) Hamza, Eman and Sims, Robert and Stolz, Günter
Summability in general Carleman ultraholomorphic classes J. Math. Anal. Appl. 430 1175--1206 (2015) Lastra, Alberto and Malek, Stéphane and Sanz, Javier
Filtering of multidimensional semiperiodic signals IEEE Transactions on Signal Processing 46 3140-3142 (1998) Félix Galindo Soto, Javier Sanz Gil
Strongly regular sequences and proximate orders J. Math. Anal. Appl. 438 920--945 (2016) Jiménez-Garrido, Javier and Sanz, Javier
Strongly regular multi-level solutions of singularly perturbed linear partial differential equations Results Math. 70 581--614 (2016) Lastra, A. and Malek, S. and Sanz, J.
Tip-tilt restoration of a segmented optical mirror using a geometric sensor Optical Engineering 52 056601 (2013) J. José Fernández-Valdivia; Alberto Lastra; Sergio Chueca; Javier Sanz; José Manuel Rodríguez-Ramos
On the mathematical basis of the Dirac formulation of quantum mechanics Internat. J. Theoret. Phys. 42 2225--2254 (2003) Gadella, M. and Gómez, F.
The Lippmann-Schwinger equations in the rigged Hilbert space J. Phys. A 35 8505--8511 (2002) Gadella, M. and Gómez, F.
A unified mathematical formalism for the Dirac formulation of quantum mechanics Found. Phys. 32 815--869 (2002) Gadella, M. and Gómez, F.
Unitary quasi-affine transforms of contractions J. Math. Anal. Appl. 351 84--96 (2009) Gómez, Fernando
Hardy class functions for potential scattering and decay Rep. Math. Phys. 62 129--143 (2008) Gadella, M. and Gómez-Cubillo, F. and Wickramasekara, S.
The stochastic limit for the hydrogen atom in interaction with the {EM} field Internat. J. Theoret. Phys. 47 2415--2429 (2008) Accardi, L. and Cubillo, F. G.
Breakdown of time-reversal symmetry: intrinsic randomness, time operator, scattering J. Geom. Symmetry Phys. 11 33--40 (2008) Gómez-Cubillo, Fernando and Suchanecki, Zdzislaw
Riggings of locally compact abelian groups J. Geom. Symmetry Phys. 11 23--31 (2008) Gadella, Manuel and Gómez, Fernando and Wickramasekara, Sujeev
Self-adjoint time operators and invariant subspaces Rep. Math. Phys. 61 123--148 (2008) Gómez, Fernando
Solution of the {MPC} problem in terms of the Sz.-Nagy-Foiac s dilation theory Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 73--96 (2008) Gómez-Cubillo, F.
Modified Lévy Laplacians Russ. J. Math. Phys. 15 45--50 (2008) Gomez, F. and Smolyanov, O. G.
Master fields, drift and dispersion in the stochastic limit of quantum theory Open Syst. Inf. Dyn. 14 459--477 (2007) Accardi, L. and Cubillo, F. G.
Nonunitary similarity transformation of conservative to dissipative evolutions: intertwining without time operator J. Math. Phys. 48 043506, 19 (2007) Gómez, Fernando
Dirac formulation of quantum mechanics: recent and new results Rep. Math. Phys. 59 127--143 (2007) Gadella, M. and Gómez, F.
A measure-theoretical approach to the nuclear and inductive spectral theorems Bull. Sci. Math. 129 567--590 (2005) Gadella, Manuel and Gómez, Fernando
Point-form dynamics of quasistable states J. Math. Phys. 54 072303, 41 (2013) Gadella, M. and Gómez-Cubillo, F. and Rodriguez, L. and Wickramasekara, S.
Orthonormal {MRA} wavelets: spectral formulas and algorithms Int. J. Wavelets Multiresolut. Inf. Process. 10 1250008, 19 (2012) Gómez-Cubillo, F. and Suchanecki, Z. and Villullas, S.
On lambda and time operators: the inverse intertwining problem revisited Internat. J. Theoret. Phys. 50 2074--2083 (2011) Gómez-Cubillo, F. and Suchanecki, Z. and Villullas, S.
Short range potential Schrödinger scattering Internat. J. Modern Phys. D 20 877--892 (2011) Bohm, Arno and Gadella, Manuel and Gomez-Cubillo, Fernando and Wickramasekara, Sujeev
Inner functions and local shape of orthonormal wavelets Appl. Comput. Harmon. Anal. 30 273--287 (2011) Gómez-Cubillo, F. and Suchanecki, Z.
Spectral models for orthonormal wavelets and multiresolution analysis of ^2(Bbb R)$ J. Fourier Anal. Appl. 17 191--225 (2011) Gómez-Cubillo, F. and Suchanecki, Z.
Evolution semigroups and time operators on Banach spaces J. Math. Anal. Appl. 371 454--464 (2010) Suchanecki, Z. and Gómez-Cubillo, F.
Eigenfunction expansions and transformation theory Acta Appl. Math. 109 721--742 (2010) Gadella, Manuel and Gómez-Cubillo, Fernando
Proyectos:
Otros datos: