6533b81ffe1ef96bd127712f
RESEARCH PRODUCT
Singular Perturbations and Operators in Rigged Hilbert Spaces
Salvatore Di BellaCamillo Trapanisubject
Discrete mathematicsPure mathematicsGeneral Mathematics010102 general mathematicsHilbert spacePerturbation (astronomy)Rigged Hilbert spaceOperator theorySpecial class01 natural sciencesregular operator010101 applied mathematicssymbols.namesakeOperator (computer programming)Singularityrigged Hilbert spaceSettore MAT/05 - Analisi Matematicasymbolssingular operator0101 mathematicsMathematicsdescription
A notion of regularity and singularity for a special class of operators acting in a rigged Hilbert space \({\mathcal{D} \subset \mathcal{H}\subset \mathcal{D}^\times}\) is proposed and it is shown that each operator decomposes into a sum of a regular and a singular part. This property is strictly related to the corresponding notion for sesquilinear forms. A particular attention is devoted to those operators that are neither regular nor singular, pointing out that a part of them can be seen as perturbation of a self-adjoint operator on \({\mathcal{H}}\). Some properties for such operators are derived and some examples are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-06-17 |