Since 2019 Ghent Analysis & PDE Center (GAPC) has been organising international workshops, conferences, seminars, and other scientific events covering a wide range of pioneering topics in Analysis and PDEs. In the winter of 2023, the GAPC decided to collect and publish mathematical results presented by women mathematician hosted at the center. This collection, in the form short papers, presented in the current book offers a wide range of state of art in Analysis and PDEs and disseminates the scientific discoveries of GAPC's visitors and members to scientists outside of the center. The short…mehr
Since 2019 Ghent Analysis & PDE Center (GAPC) has been organising international workshops, conferences, seminars, and other scientific events covering a wide range of pioneering topics in Analysis and PDEs. In the winter of 2023, the GAPC decided to collect and publish mathematical results presented by women mathematician hosted at the center. This collection, in the form short papers, presented in the current book offers a wide range of state of art in Analysis and PDEs and disseminates the scientific discoveries of GAPC's visitors and members to scientists outside of the center. The short papers published in current volume in the subseries Research Perspectives Ghent Analysis and PDE Center within the book series Trends in Mathematics are peer-reviewed written versions of the talks presented by women at GAPC events and are grouped accordingly. The current volume is strictly speaking in the realm of pure mathematics, but aims to be of interest not only to scientists in the field, butalso to anyone who has an interest to other applied sciences that Analysis and PDEs have applications to. The collection will also include the talks given at the two workshops "Women in Generalised Functions", organised in 2022 and 2023.
Mariana Chatzakou is a postdoctoral researcher at Ghent University. She obtained her PhD in mathematics in 2020 at Imperial College London. Her research interests concern the areas of harmonic analysis, non-commutative analysis, pseudo-differential operators, functional inequalities on Lie groups, and PDEs with very strong singularities. Michael Ruzhansky is a Senior Full Professor of Mathematics at Ghent University in Belgium, and a Professor of Mathematics at Queen Mary University of London in the United Kingdom. His research interests mainly lie in Partial Differential Equations, Microlocal and Harmonic Analysis, and Pseudo-Differential Operators on Lie Groups and Manifolds. Previously, he had appointments at Utrecht University, Johns Hopkins University, University of Edinburgh, and Imperial College London. He is the recipient of various awards and fellowships, notably, the Ferran Sunyer i Balaguer Prize in 2014 and 2018, Daiwa Adrian Prize in 2010, and the ISAAC award in 2007. He is serving as the head of the Ghent Analysis & PDE Center of Ghent University. Diana Stoeva is a senior postdoctoral researcher at the University of Vienna. She obtained her PhD in mathematics in 2006 at the Higher Attestation Commission of Bulgaria and her Habilitation at the University of Architecture, Civil Engineering and Geodesy in Bulgaria. Her research interests lie in functional analysis, geometry of Banach spaces, frame theory, operator theory, and Gabor and wavelet theory.
Inhaltsangabe
- Dynamical sampling for PDEs.- Mckean-Vlasov SPDES with additive noise as limits of weighted interacting particle systems.- Strong Birkhoff-James orthogonality of compact operators on Hilbert spaces.- Constructions of dual frames compensating for erasures with implementation.- On Differential Systems in Sobolev spaces with Generic Inhomogeneous Boundary Conditions.- Amenability of Semihypergroups.- On Pseudo-difference operators on the Lattice Zn.- Coercive inequalities on step-two Carnot groups.- The Laplace transform in Dunkl theory.- Asympotic analysis for generalized functions using frames.- On octonionic harmonic projection operator.- Generalised Fock spaces.- Time-frequency analysis and metaplectic operators.- A characterization of compact weighted SG pseudo-differential operators.- Global analytic solutions and symmetric waves of the 0-equation.- On the Green's function of the perturbed Laplace-Beltrami operator with a finite number of punctured points on the two-dimensional sphere.- Mixed boundary value problems for the Helmholtz equation in a model 2D double angular domain.- On hyperbolic equations with space-dependent coefficients: C well-posedness and Levi conditions.- Covering numbers of the unit ball of reproducing kernel Hilbert space of zonal positive definite kernels.- Recent examples of hypersemitoric systems and first steps towards a classification: a brief survey.- The spaces of ultradistributions over Rd+ and the Weyl calculus of pseudo-differential operators.- Nonlinear Control Problems with Fractional Derivatives.- Some Generalizations of Fixed Circle.- Investigating some measurements on the optimal dual frames for erasures.- A Short Essay on the Special Functions of Fractional Calculus.- Quantum dissipative systems in infinite dimensions.- Operator semigroups and generators associated to stochastic processes.- Strong and weak type estimates for the Littlewood-Paleyoperator g , with non-convolution kernel.- Generalized holomorphic functions: sketches of a new theory.- On an inverse time-dependent control function problem for the time-fractional diffusion equation.- Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces.- A brief excursus on mixed operators in peridynamics.- On some local and nonlocal variational problems.- Virus diffusion modeling via fractional stochastic differential equations.- Acoustic wave propagation through a cluster of hard upright cylinders: porous media and radiative transfer approach.- A note on Hardy inequality in metric measure space for the case p = 1.- Coincidence degree and fixed point theory applied to the study of solutions of a nonlinear fractional boundary value problem.- Degenerate diffusion equation with the Hadamard time-fractional derivative.- On the multipliers of Fourier series in the generalized Haar system.- Hardy Inequalities on metric measure spaces for different indices p and q.- Geometric Interpolations for Fourier multipliers on groups.- On scattering for critical NLS on waveguide manifolds: a short survey.- Exponential growth of solution for a class of reaction-diffusion equations with memory term.
- Dynamical sampling for PDEs.- Mckean-Vlasov SPDES with additive noise as limits of weighted interacting particle systems.- Strong Birkhoff-James orthogonality of compact operators on Hilbert spaces.- Constructions of dual frames compensating for erasures with implementation.- On Differential Systems in Sobolev spaces with Generic Inhomogeneous Boundary Conditions.- Amenability of Semihypergroups.- On Pseudo-difference operators on the Lattice Zn.- Coercive inequalities on step-two Carnot groups.- The Laplace transform in Dunkl theory.- Asympotic analysis for generalized functions using frames.- On octonionic harmonic projection operator.- Generalised Fock spaces.- Time-frequency analysis and metaplectic operators.- A characterization of compact weighted SG pseudo-differential operators.- Global analytic solutions and symmetric waves of the 0-equation.- On the Green's function of the perturbed Laplace-Beltrami operator with a finite number of punctured points on the two-dimensional sphere.- Mixed boundary value problems for the Helmholtz equation in a model 2D double angular domain.- On hyperbolic equations with space-dependent coefficients: C well-posedness and Levi conditions.- Covering numbers of the unit ball of reproducing kernel Hilbert space of zonal positive definite kernels.- Recent examples of hypersemitoric systems and first steps towards a classification: a brief survey.- The spaces of ultradistributions over Rd+ and the Weyl calculus of pseudo-differential operators.- Nonlinear Control Problems with Fractional Derivatives.- Some Generalizations of Fixed Circle.- Investigating some measurements on the optimal dual frames for erasures.- A Short Essay on the Special Functions of Fractional Calculus.- Quantum dissipative systems in infinite dimensions.- Operator semigroups and generators associated to stochastic processes.- Strong and weak type estimates for the Littlewood-Paleyoperator g , with non-convolution kernel.- Generalized holomorphic functions: sketches of a new theory.- On an inverse time-dependent control function problem for the time-fractional diffusion equation.- Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces.- A brief excursus on mixed operators in peridynamics.- On some local and nonlocal variational problems.- Virus diffusion modeling via fractional stochastic differential equations.- Acoustic wave propagation through a cluster of hard upright cylinders: porous media and radiative transfer approach.- A note on Hardy inequality in metric measure space for the case p = 1.- Coincidence degree and fixed point theory applied to the study of solutions of a nonlinear fractional boundary value problem.- Degenerate diffusion equation with the Hadamard time-fractional derivative.- On the multipliers of Fourier series in the generalized Haar system.- Hardy Inequalities on metric measure spaces for different indices p and q.- Geometric Interpolations for Fourier multipliers on groups.- On scattering for critical NLS on waveguide manifolds: a short survey.- Exponential growth of solution for a class of reaction-diffusion equations with memory term.
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