Search results for " coefficient problem."

showing 2 items of 2 documents

Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group

2009

Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.

General MathematicsMathematical analysisMathematics::Classical Analysis and ODEsLocally compact groupFourier integral operatorsymbols.namesakeFourier transformSettore MAT/05 - Analisi MatematicaFourier analysisImproper integralsymbolsAbelian groupCompact zero-dimensional group characters of group Kurzweil-Hestock integral Perrron integral Fourier series coefficient problem.Fourier seriesConvergent seriesMathematicsTatra Mountains Mathematical Publications
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Monotonicity and local uniqueness for the Helmholtz equation

2017

This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…

Helmholtz equationMathematics::Number Theorylocalized potentialsBoundary (topology)Monotonic function01 natural sciencesDomain (mathematical analysis)inversio-ongelmat35R30 35J05symbols.namesakeMathematics - Analysis of PDEs35J050103 physical sciencesFOS: MathematicsUniquenessHelmholtz equation0101 mathematicsinverse coefficient problemsEigenvalues and eigenvectorsMathematicsNumerical AnalysisApplied Mathematics010102 general mathematicsMathematical analysisMathematics::Spectral Theorymonotonicitystationary Schrödinger equation35R30Helmholtz free energyBounded functionsymbols010307 mathematical physicsmonotonicity localized potentialsAnalysisAnalysis of PDEs (math.AP)
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