图书简介
This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis
Part I Geometric Analysis.- Analysis on noncompact manifolds and index theory: Fredholm conditions and pseudodifferential operators.- Singular value decomposition for the X-ray transforms on the reduced Heisenberg group, and a two-radius theorem.- Nonlocal functionals with non-standard growth.- A variational approach to the hot spots conjecture.- Endpoint Sobolev inequalities for vector fields and cancelling operators.- Scattering of Maxwell potentials on curved spacetimes.- Part II. Analysis and PDEs.- Remark on the ill-posedness for KdV-Burgers equation in Fourier amalgam spaces.- Γ-convergence for the bi-Laplace-Beltrami equation on hypersurfaces.- Bounded weak solutions with Orlicz space data: an overview.- Recent progress on the mathematical theory of wave turbulence.- Laplace-Beltrami equation on Lipschitz hypersurfaces in the generic Bessel potential spaces.- On the convergence Fourier series and greedy algorithm by multiplicative system.- Asymptotics of harmonic functions in the absence of monotonicity formulas.- Semiregular non-commutative harmonic oscillators: Some spectral asymptotic properties.- Global compactness, subcritical approximation of the Sobolev quotient, and a related concentration result in the Heisenberg group.- A note on Carleson-Hunt type theorems for Vilenkin-Fourier series.- Self-similar gravitational collapse for polytropic stars.- Control of parabolic equations with inverse square infinite potential wells.- On geometric estimates for some problems arising from modeling pull-in voltage in MEMS.- A note on fractional powers of the Hermite operator.- Non-standard version of Egorov algebra of generalized functions.- Density conditions for coherent state subsystems of nilpotent Lie groups.- Space-time mixed norm estimates in Riemannian symmetric spaces of non-compact type.- Analysis on compact symmetric spaces: eigenfunctions and nonlinear Schr¨odinger equations.- Part III Applied Mathematics.- On empirical Bayes approach to inverse problems.- The interferon influence on the infection wave propagation.- Machine learning-based analysis of human motions for Parkinson’s disease diagnostics.
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