A field theoretic operator model and CowenDouglas class
Abstract
In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rankone selfcommutator acting on a Hilbert space is developed. By taking advantage of the refined existing theory of the principal function of a hyponormal operator we transfer the whole action outside the spectrum, on the resolvent of the underlying operator, localized at a distinguished vector. The whole construction turns out to rely on an elementary algebra body involving analytic multipliers and Cauchy transforms. A natural field theory interpretation of the resulting resolvent functional model is proposed.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.12409
 arXiv:
 arXiv:1810.12409
 Bibcode:
 2018arXiv181012409G
 Keywords:

 Mathematics  Functional Analysis;
 Mathematical Physics;
 Mathematics  Complex Variables;
 Mathematics  Operator Algebras;
 47B20;
 30A31;
 76C05