Staff Profile

Professional Appointments:

2024-present: Reader in Pure Mathematics, School of Mathematics, Statistics and Physics, Newcastle University, UK.

2022-2024: Senior Lecturer in Pure Mathematics, School of Mathematics, Statistics and Physics, Newcastle University, UK.

2016-2022: Lecturer in Pure Mathematics, School of Mathematics, Statistics and Physics, 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. 

• Articles

  • Colombo F, Gantner J, Kimsey DP, Sabadini I. Universality property of the S-functional calculus, noncommuting matrix variables and Clifford operators. Advances in Mathematics 2022, 410(Part A), 108719.
  • Colombo F, Kimsey DP. The spectral theorem for normal operators on a Clifford module. Analysis and Mathematical Physics 2022, 12(1), 25.
  • Kimsey DP. The matricial subnormal completion problem. Linear Algebra and Its Applications 2022, 645, 170-193.
  • Kimsey DP, Trachana M. On a Solution of the Multidimensional Truncated Matrix-Valued Moment Problem. Milan Journal of Mathematics 2022, 90, 17-101.
  • Kimsey DP, Putinar M. The moment problem on curves with bumps. Mathematische Zeitschrift 2021, 298, 935-942.
  • Kimsey DP, Putinar M. Complex Orthogonal Polynomials and Numerical Quadrature via Hyponormality. Computational Methods and Function Theory 2018, 18(3), 495-510.
  • 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. Wiener algebra for the quaternions. Mediterranean Journal of Mathematics 2016, 13(5), 2463–2482.
  • 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. The Spectral Theorem for Unitary Operators Based on the S-Spectrum. Milan Journal of Mathematics 2016, 84(1), 41-61.
  • 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. Quaternion-valued positive definite functions on locally compact Abelian groups and nuclear spaces. Applied Mathematics and Computation 2016, 286.
  • 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, Bozejko M, Colombo F, Kimsey DP, Sabadini I. Boolean convolution in the quaternionic setting. Linear Algebra and its Applications 2016, 506, 382-412.
  • 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.
  • 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.
  • 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, 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.
  • Kimsey DP. A moment matrix method for constructing cubature rules in the complex plane with prescribed size. 2015. Submitted.
  • 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. The cubic complex moment problem. Integral Equations and Operator Theory 2014, 80(3), 353-378.
  • Kimsey DP. An operator-valued generalization of Tchakaloff's theorem. Journal of Functional Analysis 2014, 266(3), 1170-1184.
  • Dym H, Kimsey DP. Trace formulas for a class of truncated block Toeplitz operators. Linear Algebra and its Applications 2013, 439(10), 3070-3099.
  • 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 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.

• Book Chapters

  • Colombo F, Gantner J, Kimsey DP. Introduction. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2019, pp.1-10.
  • Colombo F, Gantner J, Kimsey DP. The S-spectrum and the S-functional calculus. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.53-74.
  • Colombo F, Gantner J, Kimsey DP. The spectral theorem for unbounded normal operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.245-254.
  • Colombo F, Gantner J, Kimsey DP. The spectral theorem for bounded normal operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.233-243.
  • Colombo F, Gantner J, Kimsey DP. The S-functional calculus for unbounded operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.125-136.
  • Colombo F, Gantner J, Kimsey DP. The H∞-functional calculus. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.137-149.
  • Colombo F, Gantner J, Kimsey DP. The F-functional calculus for unbounded operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.177-185.
  • Colombo F, Gantner J, Kimsey DP. The F-functional calculus for bounded operators. In: Spectral Theory on the S-Spectrum for Quaternionic Operators. Cham: Birkhauser, 2018, pp.151-176.
  • Colombo F, Gantner J, Kimsey DP. Spectral theory on the s-spectrum for quaternionic operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.1-356.
  • Colombo F, Gantner J, Kimsey DP. Spectral theorem for unitary operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.255-271.
  • Colombo F, Gantner J, Kimsey DP. Spectral integration in the quaternionic setting. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.273-302.
  • Colombo F, Gantner J, Kimsey DP. Spectral integrals. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.219-231.
  • Colombo F, Gantner J, Kimsey DP. Slice hyperholomorphic functions. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.11-51.
  • Colombo F, Gantner J, Kimsey DP. Quaternionic operators on a hilbert space. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.187-217.
  • Colombo F, Gantner J, Kimsey DP. Properties of the S-functional calculus for bounded operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.75-124.
  • Colombo F, Gantner J, Kimsey DP. Bounded Quaternionic Spectral Operators. In: Operator Theory: Advances and Applications. Birkhaeuser Verlag AG, 2018, pp.303-335.
  • Colombo F, Kimsey DP. A panorama on quaternionic spectral theory. In: Modern Trends in Hypercomplex Analysis. Cham: Birkhaeuser, 2016, pp.111-142.