## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 13, Number 2 (2019), 338-358.

### A field-theoretic operator model and Cowen–Douglas class

Björn Gustafsson and Mihai Putinar

#### Abstract

In resonance with a recent geometric framework proposed by Douglas and Yang, we develop a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space. 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. We propose a natural field theory interpretation of the resulting resolvent functional model.

#### Article information

**Source**

Banach J. Math. Anal., Volume 13, Number 2 (2019), 338-358.

**Dates**

Received: 27 June 2018

Accepted: 25 November 2018

First available in Project Euclid: 28 January 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1548666055

**Digital Object Identifier**

doi:10.1215/17358787-2018-0041

**Mathematical Reviews number (MathSciNet)**

MR3927877

**Zentralblatt MATH identifier**

07045462

**Subjects**

Primary: 47B20: Subnormal operators, hyponormal operators, etc.

Secondary: 30A31 76C05

**Keywords**

hyponormal operator exponential transform Cauchy transform ideal fluid flow

#### Citation

Gustafsson, Björn; Putinar, Mihai. A field-theoretic operator model and Cowen–Douglas class. Banach J. Math. Anal. 13 (2019), no. 2, 338--358. doi:10.1215/17358787-2018-0041. https://projecteuclid.org/euclid.bjma/1548666055