Search results for "Local analysis"

showing 4 items of 14 documents

Pseudodifferential operators of Beurling type and the wave front set

2008

AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.

WavefrontPseudodifferential operatorsMathematics::Complex VariablesMathematics::Operator AlgebrasApplied MathematicsMathematical analysisWave front setMicrolocal analysisMathematics::Analysis of PDEsPseudodifferential operatorWave front setType (model theory)Mathematics::Spectral TheoryAction (physics)Set (abstract data type)UltradistributionNonlinear Sciences::Pattern Formation and SolitonsAnalysisMathematicsFront (military)Journal of Mathematical Analysis and Applications
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Local heterogeneities in population growth and decline. A spatial analysis for Italian municipalities

2021

Spatially unequal demographic dynamics lead to a progressive fragility of a territory and its socio-economic system. In Italy, municipalities in demographic malaise tend to be increasingly small in size and peripheral in location, and their local spatial aggregation increased over time. A spatial approach is here proposed to investigate the dynamics across time and space of the population variations in Italian municipalities. Global and local spatial autocorrelation analysis and several models of regression were run using as study variable the average growth rates at municipality level. The spatial autocorrelation of the study variable is quite high and stable over time. The regression resu…

demographic malaise Italy spatial regression models spatial demography local analysisdemographic malaise Italy spatial lag models spatial demography local analysisSettore SECS-S/04 - Demografia
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Applications of Microlocal Analysis in Inverse Problems

2020

This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.

radon transformRadon transforminverse problemsGeneral Mathematicslcsh:Mathematics010102 general mathematicscalderón problemMicrolocal analysisDirichlet-to-Neumann mapInverse problemlcsh:QA1-93901 natural sciencesinversio-ongelmatGel’fand problem010104 statistics & probabilitymicrolocal analysisComputer Science (miscellaneous)Calculus0101 mathematicsPostgraduate levelEngineering (miscellaneous)MathematicsMathematics
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Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data

2013

The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…

ta113Applied MathematicsGeneral MathematicsOperator (physics)ta111010102 general mathematicsMathematical analysisMicrolocal analysisNumerical Analysis (math.NA)Inverse problem01 natural sciences35R30 (Primary) 35S05 35R09 35Q20 92C55Neumann series010101 applied mathematicsSobolev spaceMathematics - Analysis of PDEsRadiative transferFOS: MathematicsGravitational singularityMathematics - Numerical Analysis0101 mathematicsAnisotropyMathematicsAnalysis of PDEs (math.AP)
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