Search results for "resolvent"

showing 2 items of 32 documents

Resolvent estimates for elliptic quadratic differential operators

2011

Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.

quadratic differential operatorSemiclassical physics47A10 35P05 15A63 53D2215A6353D22spectrumMathematics - Spectral TheoryMathematics - Analysis of PDEsQuadratic equationFOS: Mathematicsnonselfadjoint operator35P05Quadratic differentialSpectral Theory (math.SP)ResolventMathematicsNumerical AnalysisMathematics::Operator AlgebrasApplied MathematicsMathematical analysisSpectrum (functional analysis)resolvent estimateMathematics::Spectral TheoryDifferential operator47A10Range (mathematics)FBI-Bargmann transformAnalysisAnalysis of PDEs (math.AP)
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Polaroid-Type Operators

2018

In this chapter we introduce the classes of polaroid-type operators, i.e., those operators T ∈ L(X) for which the isolated points of the spectrum σ(T) are poles of the resolvent, or the isolated points of the approximate point spectrum σap(T) are left poles of the resolvent. We also consider the class of all hereditarily polaroid operators, i.e., those operators T ∈ L(X) for which all the restrictions to closed invariant subspaces are polaroid. The class of polaroid operators, as well as the class of hereditarily polaroid operators, is very large. We shall see that every generalized scalar operator is hereditarily polaroid, and this implies that many classes of operators acting on Hilbert s…

symbols.namesakePure mathematicsOperator (computer programming)Scalar (mathematics)Hilbert spacesymbolsLocally compact spaceAbelian groupLinear subspaceCommutative propertyMathematicsResolvent
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