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Operators in Rigged Hilbert spaces: some spectral properties

Camillo TrapaniSalvatore Di BellaGiorgia Bellomonte

subject

Discrete mathematicsPure mathematicsResolvent set47L60 47L05Applied MathematicsRigged Hilbert spaces; Operators; Spectral theoryHilbert spaceFunction (mathematics)Resolvent formalismRigged Hilbert spaceFunctional Analysis (math.FA)Mathematics - Functional Analysissymbols.namesakeOperator (computer programming)Rigged Hilbert spaceSettore MAT/05 - Analisi MatematicaLocally convex topological vector spacesymbolsFOS: MathematicsOperatorSpectral theoryAnalysisResolventMathematics

description

A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.

yearjournalcountryeditionlanguage
2014-01-01
10.1016/j.jmaa.2013.10.025http://hdl.handle.net/10447/84404