Professor Malcolm Brown

2021

• Brown, B. M.et al. 2021. The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval. Mathematika 67(4), pp. 788-806. (10.1112/mtk.12105)
• 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)

2020

• Brown, B. M.et al. 2020. Gap localization of multiple TE‐Modes by arbitrarily weak defects. Journal of the London Mathematical Society 102(2), pp. 773-795. (10.1112/jlms.12337)
• Brown, B. M.et al. 2020. The functional model for maximal dissipative operators (translation form): an approach in the spirit of operator knots. Transactions of the American Mathematical Society 373, pp. 4145-4187. (10.1090/tran/8029)
• Bennewitz, C., Brown, M. and Weikard, R. 2020. Spectral and scattering theory for ordinary differential equations: Vol. I: Sturm–Liouville equations. Springer International Publishing.

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)

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

• 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)
• 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)

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)
• 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., 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.
• 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)