Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Umeda, Tomio
2025.
On the resolvent convergence of discrete Dirac operators on 3D cubic lattices.
Journal of Mathematical Analysis and Applications
546
(2)
, 129247.
10.1016/j.jmaa.2025.129247
|
|
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Jameel, Ghada Shuker and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2025.
Eigenvalue bounds for perturbed periodic Dirac operators.
Journal of Spectral Theory
15
(3)
, pp. 1279-1303.
10.4171/jst/556
|
|
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Higham, Nicholas J., Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2025.
Symmetry decomposition and matrix multiplication.
Linear Algebra and its Applications
710
, pp. 310-335.
10.1016/j.laa.2025.01.041
|
|
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Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2023.
Pitfalls of predicting age related traits by polygenic risk scores.
Annals of Human Genetics
87
(5)
, pp. 203-209.
10.1111/ahg.12520
|
|
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Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Umeda, Tomio
2023.
Continuum limits for discrete Dirac operators on 2D square lattices.
Analysis and Mathematical Physics
13
(46)
10.1007/s13324-023-00809-7
|
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Simmonds, Emily, Leonenko, Ganna ORCID: https://orcid.org/0000-0001-8025-661X, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024, Hill, Matthew, Myers, Amanda, Shoai, Maryam, de Rojas, Itziar, Tesi, Niccolo, Holstege, Henne, van der Flier, Wiesje, Pijnenburg, Yolande, Ruiz, Agustin, Hardy, John, van der Lee, Sven and Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483
2023.
What does heritability of Alzheimer’s disease represent?
PLoS ONE
18
(4)
, e0281440.
10.1371/journal.pone.0281440
|
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Lettington, Matthew ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl ORCID: https://orcid.org/0000-0002-0227-3024
2023.
On the sum of left and right circulant matrices.
Linear Algebra and its Applications
658
, pp. 62-85.
10.1016/j.laa.2022.10.024
|
|
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Brown, B. Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024, Shipman, Stephen P. and Wood, Ian
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
|
|
|
Higham, Nicholas J., Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2021.
Integer matrix factorisations, superalgebras and the quadratic form obstruction.
Linear Algebra and its Applications
622
, pp. 250-267.
10.1016/j.laa.2021.03.028
|
|
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Huxley, M. N., Lettington, M. C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, K. M. ORCID: https://orcid.org/0000-0002-0227-3024
2019.
On the structure of additive systems of integers.
Periodica Mathematica Hungarica
78
, pp. 178-199.
10.1007/s10998-018-00275-w
|
|
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Phillips, T. R. L., Schmidt, K. M. ORCID: https://orcid.org/0000-0002-0227-3024 and Zhigljavsky, A. ORCID: https://orcid.org/0000-0003-0630-8279
2019.
Extension of the Schoenberg theorem to integrally conditionally positive definite functions.
Journal of Mathematical Analysis and Applications
470
(1)
, pp. 659-678.
10.1016/j.jmaa.2018.10.032
|
|
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Vivian-Griffiths, Timothy, Baker, Emily, Schmidt, Karl M. ORCID: https://orcid.org/0000-0002-0227-3024, Bracher-Smith, Matthew, Walters, James ORCID: https://orcid.org/0000-0002-6980-4053, Artemiou, Andreas ORCID: https://orcid.org/0000-0002-7501-4090, Holmans, Peter ORCID: https://orcid.org/0000-0003-0870-9412, O'Donovan, Michael C. ORCID: https://orcid.org/0000-0001-7073-2379, Owen, Michael J. ORCID: https://orcid.org/0000-0003-4798-0862, Pocklington, Andrew ORCID: https://orcid.org/0000-0002-2137-0452 and Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483
2019.
Predictive modeling of schizophrenia from genomic data: Comparison of polygenic risk score with kernel support vector machines approach.
American Journal of Medical Genetics Part B: Neuropsychiatric Genetics
180
(1)
, pp. 80-85.
10.1002/ajmg.b.32705
|
|
|
Hill, Sally, Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2018.
Block representations and spectral properties of constant sum matrices.
Electronic Journal of Linear Algebra
34
, pp. 170-190.
10.13001/1081-3810.3530
|
|
|
Phillips, Tomos and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2018.
On unbounded positive definite functions.
Mathematica Pannonica
26
(2)
, pp. 33-51.
|
|
|
Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Hill, Sally
2017.
On superalgebras of matrices with symmetry properties.
Linear and Multilinear Algebra
66
(8)
, pp. 1538-1563.
10.1080/03081087.2017.1363153
|
|
|
Vronskaya-Robl, Maria and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2017.
On perturbation stability of SSA and MSSA forecasts and the supportiveness of time series.
Statistics and Its Interface
10
(1)
, pp. 33-46.
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2016.
On the asymptotics of the spectral density of radial Dirac operators with divergent potential.
Integral Equations and Operator Theory
85
, pp. 137-149.
10.1007/s00020-015-2276-8
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Umeda, Tomio
2015.
Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials.
Letters in Mathematical Physics
105
, pp. 1479-1497.
10.1007/s11005-015-0799-1
|
|
|
Brunnock, Rochelle, Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2014.
On square roots and norms of matrices with symmetry properties.
Linear Algebra and its Applications
459
, pp. 175-207.
10.1016/j.laa.2014.06.054
|
|
|
Hughes, Daniel and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2014.
Absolutely continuous spectrum of Dirac operators with square-integrable potentials.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
144
(3)
, pp. 533-555.
10.1017/S0308210512001187
|
|
|
Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483, Ghodsi, Mansoureh and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2014.
How allele frequency and study design affect association test statistics with misrepresentation errors.
Biostatistics
15
(2)
, pp. 311-326.
10.1093/biostatistics/kxt048
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Umeda, Tomio
2014.
Spectral properties of massless Dirac operators with real-valued potentials.
Presented at: Spectral and scattering theory and related topics,
Kyoto University, Japan,
14-16 December 2011.
RIMS Kôkyûroku Bessatsu B45: Spectral and Scattering Theory and Related Topics.
RIMS Kokyuroku Bessatsu.
Kyoto, Japan:
pp. 25-30.
|
|
Kerfriden, Pierre ORCID: https://orcid.org/0000-0002-7749-3996, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024, Rabczuk, T. and Bordas, Stephane Pierre Alain ORCID: https://orcid.org/0000-0001-8634-7002
2013.
Statistical extraction of process zones and representative subspaces in fracture of random composites.
International Journal for Multiscale Computational Engineering
11
(3)
, pp. 253-287.
10.1615/IntJMultCompEng.2013005939
|
|
Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Eastham, Michael S. P. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2013.
Periodic differential operators.
Operator Theory: Advances and Applications,
vol. 230.
Basel:
Birkhäuser.
|
|
Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2012.
On the HELP Inequality for Hill Operators on Trees.
Brown, Brian Malcolm, Lang, Jan and Wood, Ian 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)
|
|
Korotyaev, Evgeny L. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2011.
On the resonances and eigenvalues for a 1D half-crystal with localised impurity.
Journal für die reine und angewandte Mathematik (Crelles Journal)
2012
(670)
, pp. 217-248.
10.1515/CRELLE.2011.153
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2010.
Spectral properties of rotationally symmetric massless dirac operators.
Letters in Mathematical Physics
92
(3)
, pp. 231-241.
10.1007/s11005-010-0393-5
|
|
Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Christiansen, Jacob S. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2009.
Spectral properties of a q-Sturm–Liouville Operator.
Communications in Mathematical Physics
287
(1)
, pp. 259-274.
10.1007/s00220-008-0623-1
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279
2009.
A characterization of the arcsine distribution.
Statistics & Probability Letters
79
(24)
, pp. 2451-2455.
10.1016/j.spl.2009.08.018
|
|
Evans, William Desmond and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2009.
A discrete Hardy-Laptev-Weidl type inequality and associated Schrödinger-type operators.
Revista Matemática Complutense
22
(1)
, pp. 75-90.
|
|
Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2008.
On multiple-testing correction in genome-wide association studies.
Genetic Epidemiology
32
(6)
, pp. 567-573.
10.1002/gepi.20331
|
|
Aumann, S., Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
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, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Langer, M. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2008.
The HELP inequality on trees.
Presented at: Isaac Newton Institute for Mathematical Sciences,
Cambridge, UK,
8 January - 29 June 2007.
Published in: Exner, P., Keating, J. P., Kuchment, P. A., Sunada, T. and Teplyaev, A. eds.
Analysis on Graphs and Its Applications.
Proceedings of Symposia in Pure Mathematics
(77)
Providence, RI:
American Mathematical Society,
pp. 337-354.
|
|
Eastham, Michael S. P. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2008.
Asymptotics of the spectral density for radial dirac operators with divergent potentials.
Publications of the Research Institute for Mathematical Sciences
44
(1)
, pp. 107-129.
10.2977/prims/1207921078
|
|
Monaquel, S. J. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2007.
On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems.
Journal of Computational and Applied Mathematics
208
(1)
, pp. 82-101.
10.1016/j.cam.2006.10.043
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2006.
Exceptional coupling constants for the Coulomb-Dirac operator with anomalous magnetic moment.
Journal of Computational and Applied Mathematics
194
(1)
, pp. 17-25.
10.1016/j.cam.2005.06.022
|
|
Eastham, Michael S. P. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2005.
Absence of high-energy spectral concentration for Dirac systems with divergent potentials.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
135
(4)
, pp. 689-702.
10.1017/S0308210500004078
|
|
|
Kalf, Hubert and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2004.
Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment.
Journal of Differential Equations
205
(2)
, pp. 408-423.
10.1016/j.jde.2004.04.009
|
|
Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Eastham, Michael S. P., Hinz, Andreas M. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
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.
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2004.
On the integrability of differential equations by quadratures according to Maximovič.
Journal of Computational and Applied Mathematics
171
(1-2)
, pp. 393-410.
10.1016/j.cam.2004.01.021
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2003.
Spectral properties of Dirac systems with coefficients infinite at infinity.
RIMS Kokyuroku
1315
, pp. 24-31.
|
|
Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2003.
Approximate projectors in singular spectrum analysis.
SIAM Journal on Matrix Analysis and Applications (SIMAX)
24
(4)
, pp. 932-942.
10.1137/S0895479801398967
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2003.
Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit.
Proceedings Of The American Mathematical Society
131
(4)
, pp. 1205-1214.
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2002.
Eigenvalues in gaps of perturbed periodic Dirac operators: numerical evidence.
Journal of Computational and Applied Mathematics
148
(1)
, pp. 169-181.
10.1016/S0377-0427(02)00580-0
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2002.
A short proof for Bargmann-type inequalities.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
458
(2027)
, pp. 2829-2832.
10.1098/rspa.2002.1021
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2001.
A remark on a paper by Evans and Harris on the point spectra of Dirac operators.
Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics
131
(A)
, pp. 1237-1243.
10.1017/S0308210500001360
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2001.
An Application of Gesztesy–Simon–Teschl Oscillation Theory to a Problem in Differential Geometry.
Journal of Mathematical Analysis and Applications
261
(1)
, pp. 61-71.
10.1006/jmaa.2001.7471
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2000.
A Remark on The Essential Spectra of Dirac Systems.
Bulletin of the London Mathematical Society
32
(1)
, pp. 63-70.
10.1112/S0024609399006463
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2000.
Relative Oscillation–Non-Oscillation Criteria for Perturbed Periodic Dirac Systems.
Journal of Mathematical Analysis and Applications
246
(2)
, pp. 591-607.
10.1006/jmaa.2000.6821
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
2000.
Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm-Liouville Operators.
Communications in Mathematical Physics
211
(2)
, pp. 465-485.
10.1007/s002200050822
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1999.
Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrodinger operators in the plane.
Proceedings of the American Mathematical Society
127
(8)
, pp. 2367-2374.
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Yamada, Osanobu
1998.
Spherically symmetric dirac operators with variable mass and potentials infinite at infinity.
Publications Of The Research Institute For Mathematical Sciences
34
(3)
, pp. 211-227.
|
|
Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Eastham, M. S. P., Hinz, A. M., Kriecherbauer, Thomas, McCormack, Daniel K. R. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1998.
Welsh Eigenvalues of radially periodic Schrödinger operators.
Journal of Mathematical Analysis and Applications
225
(1)
, pp. 347-357.
10.1006/jmaa.1998.6048
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1997.
Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity.
Mathematical Proceedings of the Cambridge Philosophical Society
122
(2)
, pp. 377-384.
|
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1996.
Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential.
Proceedings of the Royal Society of Edinburgh, Section: A Mathematics
126
(5)
, pp. 1087-1096.
10.1017/S0308210500023271
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1995.
A remark on boundary value problems for the Dirac operator.
Quarterly Journal of Mathematics
46
(184)
, pp. 509-516.
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1995.
Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators.
Forum Mathematicum
7
(7)
, pp. 459-475.
10.1515/form.1995.7.459
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1993.
On the essential spectrum of Dirac operators with spherically symmetric potentials.
Mathematische Annalen
297
(1)
, pp. 117-131.
10.1007/BF01459491
|
|
Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024
1993.
On the genericity of nonvanishing instability intervals in periodic Dirac systems.
Annales De L'Institut Henri Poincare-Physique Theorique
59
(3)
, pp. 315-326.
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|



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