Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis [PDF]
Journal of Mathematical Analysis and Applications, 2019 We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the ∂ ‾ -derivative near the real domain.
Stefan Fürdös +3 more
semanticscholar +1 more source
The Multifractal Nature of Volterra-L\'{e}vy Processes [PDF]
, 2014 We consider the regularity of sample paths of Volterra-L\'{e}vy processes. These processes are defined as stochastic integrals $$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, $$ where $X$ is a L\'{e}vy process and $F$ is a deterministic real ...
Neuman, Eyal
core +1 more source
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: Microlocal analysis [PDF]
Journal of Differential Equations, 2020 In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for solutions that allows
Claudia Garetto +2 more
semanticscholar +1 more source
Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions [PDF]
, 2014 We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic ...
Christopher, D. Sogge, Matthew D. Blair
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Microlocal Analysis of Quantum Fields on Curved Spacetimes [PDF]
, 2019 These lecture notes give an exposition of microlocal analysis methods in the study of Quantum Field Theory on curved spacetimes. We concentrate on free fields and the corresponding quasi-free states and mainly on Klein-Gordon fields.
C. G'erard
semanticscholar +1 more source
Microlocal Analysis of a Compton Tomography Problem [PDF]
SIAM Journal of Imaging Sciences, 2019 Here we present a novel microlocal analysis of a new toric section transform which describes a two dimensional image reconstruction problem in Compton scattering tomography and airport baggage screening.
James W. Webber, E. T. Quinto
semanticscholar +1 more source
Spectral asymptotics for sub-Riemannian Laplacians. I: quantum ergodicity and quantum limits in the 3D contact case [PDF]
, 2017 This is the first paper of a series in which we plan to study spectral asymptotics for sub-Riemannian Laplacians and to extend results that are classical in the Riemannian case concerning Weyl measures, quantum limits, quantum ergodicity, quasi-modes ...
de Verdière, Yves Colin +2 more
core +3 more sources
Microlocal Analysis of the Bulk-Edge Correspondence [PDF]
Communications in Mathematical Physics, 2019 The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods.
A. Drouot
semanticscholar +1 more source
A Multitarget Land Use Change Simulation Model Based on Cellular Automata and Its Application
Abstract and Applied Analysis, 2014 Based on the analysis of the existing land use change simulation model, combined with macroland use change driving factors and microlocal land use competition, and through the application of Python language integrated technical approaches such as CA, GIS,
Jun Yang +4 more
doaj +1 more source
Adiabatic Limit, Heat Kernel and Analytic Torsion [PDF]
, 2018 We study the uniform behavior of the heat kernel under the adiabatic limit using microlocal analysis and apply it to derive a formula for the analytic torsion.
Dai, Xianzhe, Melrose, Richard B
core +1 more source