# Staff Profile

## Dr David Kimsey

### Lecturer in Pure Mathematics

- Email: david.kimsey@ncl.ac.uk
- Telephone: +44 (0) 191 208 8639

#### Professional Appointments:

2016-present: Lecturer in Pure Mathematics, School of Mathematics and Statistics, Newcastle University, UK.

2013-2015: Postdoctoral fellow in the Department of Mathematics, Ben-Gurion University of the Negev, Israel. Supervisor: Daniel Alpay.

2011-2013: Postdoctoral fellow in the Faculty of Mathematics, Weizmann Institute of Science, Israel. Supervisor: Harry Dym.

#### Education:

2011: PhD in Mathematics from Drexel University, USA. Thesis title:* *Matrix-valued moment problems. Supervisor: Hugo J. Woerdeman.

2007: BSc in Mathematics from Drexel University, USA.

#### Languages:

English

Broadly speaking, my research interests center around investigating connections between operator theory on quaternionic (complex) Hilbert spaces and quaternion-valued (complex-valued) function theory. In particular, multidimensional moment problems, orthogonal matrix polynomials and related asymptotics and spectral theory for operators on a quaternionic Hilbert space.

Spectral theory for normal operators on a quaternionic Hilbert space is motivated by connections to quantum mechanics and is quite delicate due to the noncommutativity of the quaternions. One quickly realises that the notion of spectrum is not immediately obvious. The proper notion turns out to be given by the recently discovered S-spectrum. In the recent paper, Alpay, Colombo and I produced a rigorous analogue of the spectral theorem for bounded and unbounded normal operators on a quaternionic Hilbert space. Related function theory and moment problems in quaternionic settings are also of interest and have been explored.

- Colombo F, Kimsey DP. A panorama on quaternionic spectral theory.
*In: Modern Trends in Hypercomplex Analysis*. Cham: Birkhaeuser, 2016, pp.111-142. - Alpay D, Bozejko M, Colombo F, Kimsey DP, Sabadini I. Boolean convolution in the quaternionic setting.
*Linear Algebra and its Applications*2016,**506**, 382-412. - Dym H, Kimsey DP. CMV matrices, a matrix version of Baxter's theorem, scattering and de Branges spaces.
*EMS Surveys in Mathematical Sciences*2016,**3**(1), 1–105. - Alpay D, Colombo F, Gantner J, Kimsey DP. Functions of the infinitesimal generator of a strongly continuous quaternionic group.
*Analysis and Applications*2017,**15**(2), 279. - Alpay D, Colombo F, Kimsey DP, Sabadini I. Quaternion-valued positive definite functions on locally compact Abelian groups and nuclear spaces.
*Applied Mathematics and Computation*2016,**286**. - Alpay D, Colombo F, Kimsey DP. The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum.
*Journal of Mathematical Physics*2016,**57**(2), 023503. - Alpay D, Colombo F, Kimsey DP, Sabadini I. The Spectral Theorem for Unitary Operators Based on the S-Spectrum.
*Milan Journal of Mathematics*2016,**84**(1), 41-61. - Kimsey DP. The subnormal completion problem in several variables.
*Journal of Mathematical Analysis and Applications*2016,**434**, 1504-1532. - Alpay D, Colombo F, Kimsey DP, Sabadini I. Wiener algebra for the quaternions.
*Mediterranean Journal of Mathematics*2016,**13**(5), 2463–2482. - Kimsey DP.
**A moment matrix method for constructing cubature rules in the complex plane with prescribed size**. 2015. Submitted. - Alpay D, Colombo F, Kimsey DP, Sabadini I. An extension of Herglotz's theorem to the quaternions.
*Journal of Mathematical Analysis and Applications*2015,**421**(1), 754-778. - Abu-Ghanem K, Alpay D, Colombo F, Kimsey DP, Sabadini I. Boundary interpolation for slice hyperholomorphic Schur functions.
*Integral Equations Operator Theory*2015,**82**(2), 223-248. - Alpay D, Jorgensen PET, Kimsey DP. Moment problems in an infinite number of variables.
*Infinite Dimensional Analysis, Quantum Probability and Related Topics*2015,**18**(4), 1550024. - Kimsey DP. An operator-valued generalization of Tchakaloff's theorem.
*Journal of Functional Analysis*2014,**266**(3), 1170-1184. - Kimsey DP. The cubic complex moment problem.
*Integral Equations and Operator Theory*2014,**80**(3), 353-378. - Dym H, Kimsey DP. Trace formulas for a class of vector-valued Wiener-Hopf like operators, II.
*Journal of Functional Analysis*2014,**266**(2), 713-732. - Kimsey DP, Woerdeman HJ. The truncated matrix-valued
*K*-moment problem on R^{d}, C^{d}and T^{d}.*Transactions of the American Mathematical Society*2013,**365**(10), 5393-5430. - Dym H, Kimsey DP. Trace formulas for a class of truncated block Toeplitz operators.
*Linear Algebra and its Applications*2013,**439**(10), 3070-3099. - Dym H, Kimsey DP.
**Trace formulas for a class of vector-valued Wiener-Hopf like operators, I**.*Indag. Math. (N.S.)*2012,**23**, 1129-1153. - Kimsey DP, Woerdeman HJ.
**Minimal normal and commuting completions**.*International Journal of Information & Systems Sciences*2008, 50–59. - Alpay D, Bozejko M, Colombo F, Kimsey DP, Sabadini I. Boolean convolution in the quaternionic setting.
*Linear Algebra and its Applications*2016,**506**, 382-412. - Kimsey DP, Putinar M.
**Complex Orthogonal Polynomials and Numerical Quadrature via Hyponormality**.*Computational Methods and Function Theory*2018,**18**(3), 495-510.