Mathematics publications 1995-2001
All my most recent mathematical papers are to be found in the spectral theory section of the arXiv
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L^p spectral independence and L^1 analyticity.
- J. London Math. Soc (2) 52 (1995) 177-184.
- Long time asymptotics of fourth order parabolic equations.
- J. d'Analyse Math. 67 (1995) 323-345.
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Non-Gaussian aspects of heat kernel behaviour.
- J. London Math. Soc. (2) 55 (1997) 105-125.
- Uniformly elliptic operators with measurable coefficients.
- J. Functional Anal. 132 (1995) 141-169.
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Heat kernel bounds for higher order elliptic operators.
- St. Jeans Conference Proceedings, pp III.1-III.11 May/June 1995.
- Corrections to Spectral Theory and Differential Operators. Updated September 2004
- Graduate text published by Cambridge University Press, 1995.
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Sharp bounds on heat kernels of higher order uniformly elliptic
operators.
- co-author G. Barbatis. J. Operator Theory 36 (1996) 179-198.
- Limits on L^p regularity of self-adjoint elliptic operators.
- J. Diff. Eqns. 135 (1997) 83-102.
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L^p spectral theory of higher order elliptic differential operators.
- Draft 8 of review: Bull. London Math. Soc. 29 (1997) 513-546.
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Explicit constants for Rellich inequalities in $L^p(\Omega)$.
- co-author A M Hinz. Math. Zeit. 227 (1998) 511-523.
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Kato class potentials for higher order elliptic operators.
- co-author A M Hinz. J. London Math. Soc (2) 58 (1998) 669-678.
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Trapped modes in acoustic waveguides.
- co-author L. Parnovski. Quart. J. Mech. Appl. Math. 51 (1998) 477-492.
- Spectral enclosures and complex resonances for general self-adjoint operators.
- LMS J. Comput. Math. 1 (1998) 42-74
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Pointwise lower bounds on the heat kernels of higher order elliptic operators.
- Math. Proc. Camb. Phil. Soc. 125 (1999) 105-111.
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Ground state energy of almost periodic Schrodinger operators.
- Erg. Th. Dyn. Sys. 19 (1999) 591-609.
- Pseudospectra. the harmonic oscillator and complex resonances.
- Proc. Roy. Soc. London A, 455 (1999) 585-599.
- Semi-classical states for non-self-adjoint Schrodinger operators.
- Commun. Math. Phys. 200 (1999) 35-41.
- A review of Hardy Inequalities, in 'Conference in honour of V G Maz'ya, Rostock, 1998'.
- Operator Theory: Advances and Applications, vol. 110, Birkhauser Verlag, Basel, 1999.
- The computation of thresholds for Schrodinger operators.
- LMS J. Comput. Math. 2 (1999) 139-154.
- Computational spectral theory. pp 76-94 in 'Spectral Theory and Geometry', eds. E B Davies and Y Safarov.
- London Math. Soc. Lecture Notes, Ser. no. 273, Camb. Univ. Press, Camb. 1999.
- A hierarchical method for obtaining eigenvalue enclosures.
- Math. of Comp. 69 (2000) 1435-1455.
- Pseudospectra of differential operators.
- J.Oper. Theory 43 (2000) 243-262.
- Sharp boundary estimates for elliptic operators.
- Math. Proc. Camb. Phil. Soc. 129 (2000) 165-178.
- Spectral instability for some Schrodinger operators.
- co-author A Aslanyan. Numer. Math. 85 (2000) 525-552.
- Wild spectral behaviour of anharmonic oscillators.
- Bull. London Math. Soc 32 (2000) 432-438.
- A numerical investigation of the solution of a class of fourth order eigenvalue problems.
- co-authors B M Brown, P J Jimack, M D Mihajlovic.
- Proc. Roy. Soc. London A 456 (2000) 1505-1521.
- Bounds on complex eigenvalues and resonances.
- co-authors A A Abramov and A Aslanyan.
- J. Phys. A 34 (2001) 57-72.
- Spectral properties of random non-self-adjoint matrices and operators.
- Proc. Roy. Soc. London A 457 (2001) 191-206.
- Spectral theory of pseudo-ergodic operators.
- Commun. Math. Phys. 216 (2001) 687-704.
- Discrete nodal domain theorems.
- co-authors G M L Gladwell, J Leydold, P F Stadler.
- Linear Alg. and Appl. 336 (2001) 51-60.
- Separation of variables in deformed cylinders.
- co-author A Aslanyan. J. Comput. Phys. 174 (2001) 327-344.