Professor Malcolm Brown

2020

• Brown, B. M.et al. 2020. This paper considers the propagation of TE‐modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. Using the Floquet–Bloch theory in negative‐order Sobolev spaces, we characterize the precise number of eigenvalues created by the line defect in terms of the band functions of the original periodic background medium for arbitrarily weak defects.. Journal of the London Mathematical Society (10.1112/jlms.12337)

2019

• Brown, B. M.et al. 2019. Weyl solutions and j-selfadjointness for Dirac operators. Journal of Mathematical Analysis and Applications 480(2), article number: 123344. (10.1016/j.jmaa.2019.07.034)
• Brown, B. M.et al. 2019. The detectable subspace for the Friedrichs model. Integral Equations and Operator Theory 91, article number: 49. (10.1007/s00020-019-2548-9)
• 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)
• Walker, D. W.et al. 2019. Accelerating magnetic induction tomography-based imaging through heterogeneous parallel computing. Concurrency and Computation: Practice and Experience 31(17), article number: e5265. (10.1002/cpe.5265)
• Alberti, G. S.et al. 2019. Essential spectrum for Maxwell's equations. Annales Henri Poincaré 20, pp. 1471-1499. (10.1007/s00023-019-00762-x)
• Brown, B. M., Langer, H. and Tretter, C. 2019. Compressed resolvents and reduction of spectral problems on star graphs. Complex Analysis and Operator Theory 13(1), pp. 291-320. (10.1007/s11785-018-0793-6)
• Brown, B. M.et al. 2019. The functional model for maximal dissipative operators (translation form): an approach in the spirit of operator knots. Transactions of the American Mathematical Society

2017

• Brown, B. M.et al. 2017. Gap localization of TE-Modes by arbitrarily weak defects. Journal of the London Mathematical Society 95(3), pp. 942-962. (10.1112/jlms.12046)
• Brown, B. M.et al. 2017. Inverse problems for boundary triples with applications. Studia Mathematica 237(3), pp. 241-275. (10.4064/sm8613-11-2016)

2016

• Brown, M., Marletta, M. and Symons, F. 2016. Uniqueness from discrete data in an inverse spectral problem for a pencil of ordinary differential operators. Journal of the London Mathematical Society 94(3), pp. 793-813. (10.1112/jlms/jdw059)
• Brown, B. M.et al. 2016. Detectable subspaces and inverse problems for Hain-Lüst-type operators. Mathematische Nachrichten 289(17-18), pp. 2108-2132. (10.1002/mana.201500231)
• Bennewitz, C., Brown, B. M. and Weikard, R. 2016. The spectral problem for the dispersionless Camassa-Holm equation. Presented at: International Workshop on Operator Theory and Applications, Amsterdam, The Netherlands, 14-18 July 2014 Presented at Eisner, T. et al. eds.Operator Theory, Function Spaces, and Applications: International Workshop on Operator Theory and Applications, Amsterdam, July 2014. Operator Theory: Advances and Applications Springer pp. 67-90., (10.1007/978-3-319-31383-2_4)
• 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)
• Brown, B. M., Marletta, M. and Reyes Gonzales, J. M. 2016. Uniqueness for an inverse problem in electromagnetism with partial data. Journal of Differential Equations 260(8), pp. 6525-6547. (10.1016/j.jde.2016.01.002)

2015

• Brown, B. M.et al. 2015. On the spectrum of waveguides in planar photonic bandgap structures. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471(2176), article number: 20140673. (10.1098/rspa.2014.0673)

2014

• Brown, B. M.et al. 2014. Spectrum created by line defects in periodic structures. Mathematical News / Mathematische Nachrichten 287(17-18), pp. 1972-1985. (10.1002/mana.201300165)
• Boegli, S.et al. 2014. Guaranteed resonance enclosures and exclosures for atoms and molecules. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470(2171), article number: 20140488. (10.1098/rspa.2014.0488)

2013

• Brown, B. M., Langer, H. and Langer, M. 2013. Bessel-type operators with an inner singularity. Integral Equations and Operator Theory 75(2), pp. 257-300. (10.1007/s00020-012-2023-3)
• Brown, B. M., Eastham, M. S. P. and Schmidt, K. M. 2013. Periodic differential operators. Operator Theory: Advances and Applications Vol. 230. Basel: Birkhäuser.

2012

• Brown, B. M. and Schmidt, K. M. 2012. On the HELP Inequality for Hill Operators on Trees. In: Brown, B. M., Lang, J. and Wood, I. G. eds. Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends. Operator Theory: Advances and Applications Vol. 219. Basel: Springer, pp. 21-36., (10.1007/978-3-0348-0263-5_2)
• Bennewitz, C., Brown, B. M. and Weikard, R. 2012. Scattering and inverse scattering for a left-definite Sturm–Liouville problem. Journal of Differential Equations 253(8), pp. 2380-2419. (10.1016/j.jde.2012.06.016)

2011

• Brown, B. M. and Jais, M. 2011. A variational approach to an electromagnetic inverse problem. Inverse Problems 27(4), article number: 45011. (10.1088/0266-5611/27/4/045011)

2010

• Hiscox, A. J., Brown, B. M. and Marletta, M. 2010. On the low energy behavior of Regge poles. Journal of Mathematical Physics 51(10), article number: 102104. (10.1063/1.3496811)
• Brown, B. M.et al. 2010. Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics. LMS Journal of Computation and Mathematics 13, pp. 65-81. (10.1112/S1461157008000466)

2009

• Brown, B. M., Christiansen, J. S. and Schmidt, K. M. 2009. Spectral properties of a q-Sturm–Liouville Operator. Communications in Mathematical Physics 287(1), pp. 259-274. (10.1007/s00220-008-0623-1)
• Brown, B. M., Eastham, M. . S. . P. and Wood, I. . G. 2009. Conditions for the spectrum associated with an asymptotically straight leaky wire to comprise the interval (−∞, ∞). Journal of Physics A: Mathematical and Theoretical 42(5), article number: 55207. (10.1088/1751-8113/42/5/055207)
• Brown, B. M., Naboko, S. and Weikard, R. 2009. The Inverse Resonance Problem for Hermite Operators. Constructive Approximation 30(2), pp. 155-174. (10.1007/s00365-008-9037-8)
• Hiscox, A. J., Brown, B. M. and Marletta, M. 2009. Analysis of Regge poles for the Schrodinger equation. Proceedings of The Royal Society. A. Mathematical Physical and Engineering Sciences 465(2109), pp. 2813-2823. (10.1098/rspa.2009.0091)
• Brown, B. M., Eastham, M. S. P. and Wood, I. G. 2009. Estimates for the lowest eigenvalue of a star graph. Journal of Mathematical Analysis and Applications 354(1), pp. 24-30. (10.1016/j.jmaa.2008.12.014)
• Brown, B. M., Grubb, G. and Wood, I. G. 2009. M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems. Mathematische Nachrichten 282(3), pp. 314-347. (10.1002/mana.200810740)
• Brown, B. M.et al. 2009. The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum. Integral Equations and Operator Theory 63(3), pp. 297-320. (10.1007/s00020-009-1668-z)
• Bennewitz, C., Brown, B. M. and Weikard, R. 2009. Inverse Spectral and Scattering Theory for the Half-Line Left-Definite Sturm-Liouville Problem. SIAM Journal on Mathematical Analysis 40(5), pp. 2105-2131. (10.1137/080724575)
• Brown, B. M.et al. 2009. On spectral bounds for photonic crystal waveguides. International Series of Numerical Mathematics 157, pp. 23-30. (10.1007/978-3-7643-8773-0_3)

2008

• Brown, B. M.et al. 2008. Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices. Journal of the London Mathematical Society 77(3), pp. 700-718. (10.1112/jlms/jdn006)
• Brown, B. M., Langer, M. and Schmidt, K. M. 2008. The HELP inequality on trees. Presented at: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8 January - 29 June 2007 Presented at Exner, P. et al. eds.Analysis on Graphs and Its Applications. Proceedings of Symposia in Pure Mathematics Vol. 77. Providence, RI: American Mathematical Society pp. 337-354.
• Aumann, S., Brown, B. M. and Schmidt, K. M. 2008. A Hardy-Littlewood-type inequality for the p-Laplacian. Bulletin of the London Mathematical Society 40(3), pp. 525-531. (10.1112/blms/bdn035)
• Brown, B. M. and Eastham, M. S. P. 2008. Titchmarsh's asymptotic formula for periodic eigenvalues and an extension to the p-Laplacian. Journal of Mathematical Analysis and Applications 338(2), pp. 1255-1266. (10.1016/j.jmaa.2007.06.017)
• Brown, B. M., Eastham, M. S. P. and Wood, I. G. 2008. Conditions for the spectrum associated with an asymptotically straight leaky wire to contain an interval [− α2/4, ∞). Archiv der Mathematik 90(6), pp. 554-558. (10.1007/s00013-008-2612-1)
• Brown, B. M., Eastham, M. S. P. and Wood, I. G. 2008. An example on the discrete spectrum of a star graph. Presented at: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8 January - 29 June 2007 Presented at Exner, P. et al. eds.Analysis on graphs and its applications. Proceedings of Symposia in Pure Mathematics Vol. 77. Providence, RI: American Mathematical Society pp. 331-335.

2007

• Brown, B. M. and Eastham, M. S. P. 2007. Eigenvalues of the radial p-Laplacian with a potential on (0,∞). Journal of Computational and Applied Mathematics 208(1), pp. 111-119. (10.1016/j.cam.2006.10.046)
• Brown, B. M., Lang, J. and Lewis, R. 2007. Preface. Journal of computational and applied mathematics 208(1), pp. 1-2. (10.1016/j.cam.2006.10.089)
• Brown, B. M. and Eastham, M. 2007. Bounds for the positive eigenvalues of the p-Laplacian with decaying potential. Journal of Mathematical Analysis and Applications 325(1), pp. 734-744. (10.1016/j.jmaa.2006.01.058)

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)
• Brown, B. M. and Eastham, M. . . 2006. Extensions of the Kummer evaluation of a finite hypergeometric series. Journal of computational and applied mathematics 194(1), pp. 131-140. (10.1016/j.cam.2005.06.018)
• Brown, B. M. and Eastham, M. S. P. 2006. A note on the Dixon formula for a finite hypergeometric series. Korean Journal of Computational and Applied Mathematics 194(1), pp. 173-175. (10.1016/j.cam.2005.06.021)
• Brown, B. M., Jais, M. and Kalmbach, B. M. 2006. A variational approach to inverse problems for anisotropic systems. Presented at: UAB International Conference on Differential Equations and Mathematical Physics, Birmingham, AL, USA, 29 March - 2 April 2005 Presented at Chernov, N. et al. eds.Recent Advances in Differential Equations and Mathematical Physics. Contemporary Mathematics Vol. 412. Providence, RI: American Mathematical Society pp. 87-102.

2005

• Brown, B. M. and Weikard, R. 2005. A Borg-Levinson theorem for trees. Proceedings of The Royal Society A Mathematical physical and engineering sciences 461(2062), pp. 3231-3243. (10.1098/rspa.2005.1513)
• Brown, B. M., Jais, M. and Knowles, I. . W. 2005. A variational approach to an elastic inverse problem. Inverse Problems 21(6), pp. 1953-1973. (10.1088/0266-5611/21/6/010)
• Brown, B. M., Naboko, S. and Weikard, R. 2005. The inverse resonance problem for Jacobi operators. Bulletin of the London Mathematical Society 37(5), pp. 727-737. (10.1112/S0024609305004674)
• Brown, B. M. and Christiansen, J. S. 2005. On the Krein and Friedrichs extensions of a positive Jacobi operator. Expositiones Mathematicae 23(2), pp. 179-186. (10.1016/j.exmath.2005.01.020)

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)
• Brown, B. M. and Reichel, W. 2004. Eigenvalues of the radially symmetric p-Laplacian in Rn. Journal of the London Mathematical Society 69(3), pp. 657-675. (10.1112/S002461070300512X)
• Brown, B. M. and Marletta, M. 2004. Spectral inclusion and spectral exactness for PDEs on exterior domains. IMA Journal of Numerical Analysis 24(1), pp. 21-43. (10.1093/imanum/24.1.21)
• Brown, B. M.et al. 2004. Distribution of eigenvalues in gaps of the essential spectrum of Sturm-Liouville operators - a numerical approach. Journal Of Computational Analysis And Applications 6(1), pp. 85-95.
• Brown, B. M. and Eastham, M. S. P. 2004. Extended Hurwitz results for hypergeometric functions arising in spectral theory. Journal of Computational and Applied Mathematics 171(1-2), pp. 113-121. (10.1016/j.cam.2004.01.006)
• 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)
• Brown, B. M. and Weikard, R. 2004. The inverse resonance problem for perturbations of algebro-geometric potentials. Inverse Problems 20(2), pp. 481-494. (10.1088/0266-5611/20/2/011)

2003

• Brown, B. M., Knowles, I. and Weikard, R. 2003. On the inverse resonance problem. Journal of the London Mathematical Society 68(2), pp. 383-401. (10.1112/S0024610703004654)
• 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)

2001

• Brown, B. M. and Marletta, M. 2001. Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 457(2005), pp. 117-139. (10.1098/rspa.2000.0659)
• Brown, B. M., Jimack, P. K. and Mihajlović, M. D. 2001. An efficient direct solver for a class of mixed finite element problems. Applied Numerical Mathematics 38(1-2), pp. 1-20. (10.1016/S0168-9274(00)00048-9)

2000

• Brown, B. M. and Kirby, V. G. 2000. A computational investigation of an integro-differential inequality with periodic potential. Journal of Inequalities and Applications 5(4), pp. 321-342. (10.1155/S1025583400000163)
• Brown, B. M.et al. 2000. A numerical investigation of the solution of a class of fourth-order eigenvalue problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 456(1998), pp. 1505-1521. (10.1098/rspa.2000.0573)

1998

• Brown, B. M.et al. 1998. Welsh Eigenvalues of radially periodic Schrödinger operators. Journal of Mathematical Analysis and Applications 225(1), pp. 347-357. (10.1006/jmaa.1998.6048)

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)