6533b824fe1ef96bd1280060

RESEARCH PRODUCT

Sesquilinear forms associated to sequences on Hilbert spaces

Rosario Corso

subject

Semi-framePure mathematicsGeneral MathematicsContext (language use)42C15 47A07 47A05 46C0501 natural sciencesBessel sequencesymbols.namesakeSettore MAT/05 - Analisi MatematicaRepresentation theoremFOS: MathematicsFrame (artificial intelligence)Frame0101 mathematics0105 earth and related environmental sciencesMathematicsResolvent set010505 oceanography010102 general mathematicsAssociated operatorRepresentation (systemics)Hilbert spaceFunctional Analysis (math.FA)Mathematics - Functional AnalysisBounded functionsymbolsSesquilinear forms

description

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.

yearjournalcountryeditionlanguage
2019-06-17
http://arxiv.org/abs/1812.03349