Research Interests

My research interests are principally in Operator Theory and Functional Analysis.

I currently organise the York Analysis, Geometry and Number Theory Seminar.

Publications

• Theory and Applications of Hilbert's Projective Metric to Linear and Nonlinear Problems in Positive Operator Theory D. Phil. thesis, University of Sussex (1991)
• An Integral Equation Arising From a Problem in Mathematical Biology Bull. London Math. Soc 23 (1991) 293-299
• Hilbert's Projective Metric and the Spectral Properties of Positive Linear Operators Proc. London Math. Soc. (3) 70 (1995) 411-440
• (with Roger D. Nussbaum) An Elementary Proof of the Birkhoff-Hopf Theorem Math. Proc. Camb. Phil. Soc. (1995) 117, 31-55
• (with Roger D. Nussbaum) Applications of the Birkhoff-Hopf Theorem to the Spectral Theory of Positive Linear Operators Math. Proc. Camb. Phil. Soc. (1995) 117, 491-512
• Compactness Criteria for Integral Operators in $L^\infty$ and $L^1$ spaces Proc. Amer. Math. Soc. vol. 123 no. 12 December 1995 3709-3716
• The Eigenvalue Distribution of Oscillatory and Strictly Sign-Regular Matrices Linear Algebra and its Applications 246:17-21 (1996)
• Eigenvalues of Totally Positive Integral Operators Bull. London Math. Soc. 29 (1997) 216-222
• (with C. J. Fewster) Bounds on negative energy densities in flat spacetime Phys. Rev. D58 (1998) 084010 gr-qc/9805024
• (with Bernard S. Kay) Peripheral Spectra of Order-Preserving Normal Operators Bull. London Math. Soc 31 (1999) 574-576
• Compactness Criteria and Measures of Noncompacness in Function Spaces Journal London Math. Soc. (2) 62 (2000) 263-277
• Norms of Iterates of Volterra Operators on $L^2(0,1)$, Journal of Operator Theory 50(2) (2003) 369-386.
• Norms of Iterates of Volterra Operators on $L^p(0,1)$ to appear, Integral Equations and operator Theory
• (with Christopher J. Fewster and Rainer Verch) Quantum inequalities in quantum mechanics, submitted math-ph/0312046

Last Modified: Monday, 15-Mar-2004 14:05:54 GMT