DEPARTMENT OF MATHEMATICS

 

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[Picture] Dr John Reade Dr. John Reade
Lecturer in Mathematics

Room 9.09
Department of Mathematics
University of Manchester
Email: johnr@ma.man.ac.uk
Phone: +44 (0)161 275 5832 (direct line)
Fax: +44 (0)161 275 5819

Research Interests: Eigenvalues of Integral Operators

The Spectral theorem for a compact symmetric operator on Hilbert Space defines a real null sequence of eigenvalues with an orthonormal basis of eigenfunctions. The Hille-Tamarkin programme relates asymptotic behaviour of the eigenvalues to analytic properties of the kernel of the operator.

I have been able to improve the asymptotic estimates in the case when the operator is positive definite. More recently I have collaborated with Graham Little on the nth indefinite integral operator, and with Jonathan Keating on Abel summability of gap series.

More recently still, I have been interested in rainbows, haloes and glories.  These are colour phenomena in the sky caused by refraction through raindrops and ice crystals.

Recent Publications

Estimates for the Norm of the nth Indefinite Integral Operator. Bull. London Math. Soc. Vol. 30 (1998) 539-542.

Abel Summability of Gap series. Jour. Edinburgh Math. Soc., Vol.43 (2000) pp95-101.

On the Scientific Explanation of Parhelia, Math. Gaz., Vol.87, No.509 (July 2003).

Teaching

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Page last modified: 10 September 2003