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.
- Dynamical sampling for PDEs.- Mckean-Vlasov SPDES with additive noise
as limits of weighted interacting particle systems.- Strong BirkhoffJames
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
Greens 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.
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.
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