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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
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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 2021. Correction to: Probability of Alzheimer's disease based on common and rare genetic variants. Alzheimer's Research and Therapy 13 (1) , 156. 10.1186/s13195-021-00898-1
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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 2021. Probability of Alzheimer’s disease based on common and rare genetic variants. Alzheimer's Research & Therapy 13 , 140. 10.1186/s13195-021-00884-7
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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 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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Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2021. Challenges of adjusting Single-Nucleotide Polymorphism effect sizes for linkage disequilibrium. Human Heredity 85 (1) , pp. 24-34. 10.1159/000513303
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Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2020. Divisor functions and the number of sum systems. Integers 20 , A61.
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Hill, S. L., 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 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 10.1007/s11139-018-0093-9
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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
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Baker, Emily, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024, Sims, Rebecca ORCID: https://orcid.org/0000-0002-3885-1199, O'Donovan, Michael C. ORCID: https://orcid.org/0000-0001-7073-2379, Williams, Julie ORCID: https://orcid.org/0000-0002-4069-0259, Holmans, Peter ORCID: https://orcid.org/0000-0003-0870-9412 and Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 2018. POLARIS: polygenic LD-adjusted risk score approach for set-based analysis of GWAS data. Genetic Epidemiology 42 (4) , pp. 366-377. 10.1002/gepi.22117
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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
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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.
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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
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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.
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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
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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
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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
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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
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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.

Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2013. An extremal property of the generalized arcsine distribution. Metrika 76 (3) , pp. 347-355. 10.1007/s00184-012-0391-y

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.

Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024, Vedernikov, Alexey, Owen, Michael John ORCID: https://orcid.org/0000-0003-4798-0862, Craddock, Nicholas John ORCID: https://orcid.org/0000-0003-2171-0610, Holmans, Peter Alan ORCID: https://orcid.org/0000-0003-0870-9412 and O'Donovan, Michael Conlon ORCID: https://orcid.org/0000-0001-7073-2379 2012. Permutation-based approaches do not adequately allow for linkage disequilibrium in gene-wide multi-locus association analysis. European Journal of Human Genetics 20 (8) , pp. 890-896. 10.1038/ejhg.2012.8

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

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.

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

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

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.

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

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

Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2006. Susceptibility of Biallelic Haplotype and Genotype Frequencies to Genotyping Error. Biometrics 62 (4) , pp. 1116-1123. 10.1111/j.1541-0420.2006.00563.x

Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2006. Individual SNP Allele Reconstruction from Informative Markers Selected by a Non-Linear Gauss-Type Algorithm. Human Heredity 62 (2) , pp. 97-106. 10.1159/000096097

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
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Escott-Price, Valentina ORCID: https://orcid.org/0000-0003-1784-5483, Holmans, Peter Alan ORCID: https://orcid.org/0000-0003-0870-9412, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Craddock, Nicholas John ORCID: https://orcid.org/0000-0003-2171-0610 2005. Design of Case-controls Studies with Unscreened Controls. Annals of Human Genetics 69 (5) , pp. 566-576. 10.1111/j.1529-8817.2005.00175.x

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
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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.
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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
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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.
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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.
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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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