# Professor Des Evans

Emeritus Professor of Mathematics

- evanswd@cardiff.ac.uk
- +44 (0)29 2087 4206
- E/1.09, 1st Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

## Overview

### Research interests

- Spectral Theory and Differential Operators
- Mathematical Physics
- Computational Spectral Theory
- Analysis on domains with irregular boundaries
- Function Spaces and Inequalities

### Research group

## Biography

### Education

- B.Sc. (Wales) 1961
- D.Phil. (Oxford) 1965

### Supervisors

- E.C.Titchmarsh FRS
- J.B.McLeod FRS

### Research positions

- Assistant Lecturer, UC Cardiff, 1964-65
- Lecturer, UC Cardiff, 1965-73
- Senior Lecturer, UC Cardiff, 1973-75
- Reader, University of Wales, 1975-77
- Professor of Pure Mathematics, University of Wales, 1977- present
- Emeritus Professor, Cardiff University, 2008- present

### Honours and awards

- Fellow of the Learned Society of Wales 2010/11

## Publications

### 2021

- Brown, B. M., Evans, W. D. and Wood, I. G. 2021. Non-negative extensions of Hamiltonian systems. In: Fritz Gesztesy, . and Andrei Martinez-Finkelshtein, . eds. From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory. Operator Theory: Advances and Applications Springer, pp. 15-39., (10.1007/978-3-030-75425-9_2)

### 2019

- Brown, B., Evans, W. D. and Wood, I. G. 2019. Positive self-adjoint operator extensions with applications to differential operators. Integral Equations and Operator Theory 91, article number: 41. (10.1007/s00020-019-2540-4)

### 2016

- Brown, B. M. and Evans, W. D. 2016. Selfadjoint and m sectorial extensions of Sturm-Liouville operators. Integral Equations and Operator Theory 85(2), pp. 151-166. (10.1007/s00020-016-2296-z)

### 2015

- Balinsky, A., Evans, W. D. and Roger, L. 2015. The analysis and geometry of Hardy's Inequality. Springer.

### 2013

- Edmunds, D. E., Evans, W. D. and Harris, D. J. 2013. The structure of compact linear operators in Banach spaces. Revista Mathematica Complutense 26(2), pp. 445-469. (10.1007/s13163-012-0107-x)

### 2012

- Balinsky, A., Evans, W. D. and Lewis, R. T. 2012. Hardy's inequality and curvature. Journal of Functional Analysis 262(2), pp. 648-666. (10.1016/j.jfa.2011.10.001)

### 2011

- Balinsky, A., Evans, W. D. and Umeda, T. 2011. The Dirac-Hardy and Dirac-Sobolev inequalities in L1. Publications of the Research Institute for Mathematical Sciences 47(3), pp. 791-801. (10.2977/PRIMS/51)

### 2010

- Balinsky, A. and Evans, W. D. 2010. Spectral Analysis of Relativistic Operators. London: Imperial College Press.
- Balinsky, A. and Evans, W. D. 2010. Some recent results on Hardy-type inequalities. Applied Mathematics and Information Sciences 4(2), pp. 191-208.

### 2009

- Evans, W. D. and Schmidt, K. M. 2009. A discrete Hardy-Laptev-Weidl type inequality and associated Schrödinger-type operators. Revista Matemática Complutense 22(1), pp. 75-90.

### 2008

- Balinsky, A., Evans, W. D. and Saito, Y. 2008. Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators. Journal of Mathematical Physics 49(4), article number: 43514. (10.1063/1.2912229)
- Balinsky, A., Evans, W. and Hundertmark, D. 2008. On inequalities of Hardy-Sobolev type. Banach Journal of Mathematical Analysis (BJMA) 2(2), pp. 94-106.

### 2006

- Brown, B. M. and Evans, W. D. 2006. Foreword. Journal of Computational and Applied Mathematics 194(1), pp. 1. (10.1016/j.cam.2005.06.032)

### 2005

- Evans, W. D. and Solomyak, M. 2005. Smilansky's model of irreversible quantum graphs: I. The absolutely continuous spectrum. Journal of Physics A: Mathematical and General 38(21), pp. 4611-4627. (10.1088/0305-4470/38/21/007)

### 2004

- Brown, B. M. and Evans, W. D. 2004. Preface [Editorial]. Journal of Computational and Applied Mathematics 171(1-2), pp. ix. (10.1016/j.cam.2004.01.004)
- Evans, W. D., Harris, D. J. and Saito, Y. 2004. On the approximation numbers of Sobolev embeddings on singular domains and trees. The Quarterly Journal of Mathematics 55(3), pp. 267-302. (10.1093/qmath/hag050)
- Brown, B. M., Eastham, M. S. P. and Evans, W. D. 2004. Laudatum. Journal of computational and applied mathematics 171(1-2), pp. xi-xiii. (10.1016/j.cam.2004.01.034)

### 2003

- Brown, B. M., Evans, W. D. and Plum, M. 2003. Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems. Proceedings of the London Mathematical Society 87(2), pp. 419-450. (10.1112/S0024611503014096)

### 2002

- Balinsky, A. and Evans, W. D. 2002. On the Zero Modes of Weyl-Dirac Operators and their Multiplicity. Bulletin of the London Mathematical Society 34(2), pp. 236-242. (10.1112/S0024609301008736)
- Balinsky, A. and Evans, W. D. 2002. On the spectral properties of the Brown-Ravenhall operator. Journal of Computational and Applied Mathematics 148(1), pp. 239-255. (10.1016/S0377-0427(02)00583-6)

### 2001

- Balinsky, A., Evans, W. D. and Lewis, R. T. 2001. On the number of negative eigenvalues of Schrödinger operators with an Aharanov-Bohm magnetic field. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences 457(2014), pp. 2481-2489. (10.1098/rspa.2001.0851)
- Evans, W. D., Harris, D. J. and Lang, J. 2001. The approximation numbers of Hardy-type operators on trees. Proceedings of the London Mathematical Society 83(2), pp. 390-418. (10.1112/plms/83.2.390)
- Balinsky, A. and Evans, W. D. 2001. On the zero modes of Pauli operators. Journal of Functional Analysis 179(1), pp. 120-135. (10.1006/jfan.2000.3670)
- Balinsky, A., Evans, W. D. and Lewis, R. T. 2001. Sobolev, Hardy and CLR inequalities associated with Pauli operators in R3 [Letter]. Journal of Physics A: Mathematical and General 34(5), pp. L19-L23. (10.1088/0305-4470/34/5/101)

### 1999

- Balinsky, A. and Evans, W. D. 1999. Stability of One-Electron Molecules in the Brown-Ravenhall Model. Communications in Mathematical Physics 202(2), pp. 481-500. (10.1007/s002200050592)
- Balinsky, A. and Evans, W. D. 1999. On the stability of relativistic one-electron molecules [Letter]. Journal of Physics A: Mathematical and General 32(11), pp. L129-L132. (10.1088/0305-4470/32/11/001)

### 1998

- Balinsky, A. and Evans, W. D. 1998. On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded Eigenvalues. Letters in Mathematical Physics 44(3), pp. 233-248. (10.1023/A:1007425400991)

### 1993

- Beynon, M. J., Brown, B. M. and Evans, W. D. 1993. On an Inequality of the Kolmogorov Type for a Second-Order Differential Expression. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 442(1916), pp. 555-569. (10.1098/rspa.1993.0121)

## Teaching

### Graduated (since 2000)

- R.Wilson
- A.Al-Homaidan
- S.Monaquel
- J.Thomas

### Current research projects

- Hardy and Rellich inequalities
- Zero modes of massless Dirac operators
- Representations of compact linear operators in Banach spaces and non-linear eigenvalue problems
- Spectra of the Neumann Laplacian on irregular domains
- Weighted inequalities involving rho-quasiconcave operators

### External Funding Since 2000

#### EPSRC

- GR/N20560 (£4,800) Visiting Fellowship for Professor Y. Saito, June, 2000
- GR/R37111/01 (£63,829) Spectral Theory Network, 2001-04 (with Profs B.M.Brown and E.B.Davies)
- GR/R20885/01 (£111,374) Research Assistantship for Dr R. Romanov, 2002-05 (with Drs B.M.Brown and M.Marletta)
- GR/R95586/01 (£123,595) Research Assistantship for Dr A.Tuykov, 2003-06(with Dr A.Balinsky)
- GR/S47229 (£8,113) Visiting Fellowship for Professor S. Naboko, 2004 (with Prof B.M.Brown and Dr M. Marletta)
- GR/T01556 (£8,150) Visiting Fellowship for Professor M. Solomyak, July 2004
- EP/E04834X (£3,815) Visiting Fellowship for Professor Y. Saito, April, 2007

#### Other sources

- Leverhulme Trust (F/00407/E) (£19,500) Collaborative research project with Prague Mathematics Institute, 01.03.01-29.02.04
- NATO (£6,490) (PST.CLG.978694) Collaborative research project with European groups, 01.04.02-31.03.04

### Major conference talks since 2004

- Warwick Workshop on Large Many Body Systems, 23-28 August, 2004
- Plenary lecture to ISAAC conference in Ankara, 13-18 August, 2007

#### Books

- Edmunds, D.E. and Evans, W.D. 2004. Hardy Operators, Function Spaces and Embeddings. Berlin, Heidelberg: Springer.
- Edmunds, D.E. and Evans, W.D. 2013. Representation of Linear Operators Between Banach Spaces. Heidelberg, New York, London: Birkhauser-Springer,
- Balinsky, A., Evans, W.D. and Lewis, R.T. 2015. The Analysis and Geometry of Hardy's Inequality. Berlin, London: Springer.