On vertex conditions for elastic systems JC Kiik, P Kurasov, M Usman Physics Letters A 379 (34-35), 1871-1876, 2015 | 21 | 2015 |
On some sharp spectral inequalities for Schrödinger operators on semiaxis P Exner, A Laptev, M Usman Communications in Mathematical Physics 326, 531-541, 2014 | 17 | 2014 |
Trace formulas for Schrödinger operators on the half-line S Demirel, M Usman Bulletin of Mathematical Sciences 1, 397-427, 2011 | 17 | 2011 |
-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness M Astudillo, P Kurasov, M Usman Advances in Mathematical Physics 2015, 2015 | 14 | 2015 |
Sharp spectral inequalities for fourth order differential operators on semi-axis MD Zia, M Usman Mathematical Physics, Analysis and Geometry 22 (4), 24, 2019 | 3 | 2019 |
Trace formulas for Schrödinger operators on star graphs with general matching conditions M Usman, AA Zaidi Journal of Physics. A, Mathematical and Theoretical (Online) 51 (36), 2018 | 3 | 2018 |
Perturbation determinant and Levinson's formula for Schr\" odinger operators with generalized point interaction MF Anwar, M Usman, MD Zia arXiv preprint arXiv:2301.11388, 2023 | 1 | 2023 |
A trace formula, perturbation determinant and Levinson’s theorem for a class of star graphs M Usman, MD Zia The European Physical Journal Plus 137 (6), 1-27, 2022 | 1 | 2022 |
Surgery Transformations and Spectral Estimates of Beam Operators A Ali, M Usman Mathematical Physics, Analysis and Geometry 26 (4), 27, 2023 | | 2023 |
Perturbation determinant and Levinson's formula for Schrödinger operators with generalized point interaction M Fazeel Anwar, M Usman, M Danish Zia arXiv e-prints, arXiv: 2301.11388, 2023 | | 2023 |
Surgery transformations and eigenvalue estimates for quantum graphs with vertex interactions A Ali, M Usman arXiv preprint arXiv:2201.13017, 2022 | | 2022 |
Sobolev type inequalities for compact metric graphs M Usman Journal of Inequalities and Applications 2018 (1), 271, 2018 | | 2018 |
Trace formulae and spectral inequalities for a class of differential operators M Usman Imperial College London, 2013 | | 2013 |