Muhammad Usman

activity

20112023

most citedOn some sharp spectral inequalities for Schrödinger operators on semi-axis

11 citations · 11 across the 4 of their papers we have counts for

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Showing 2022Show all

2 papers · 1 filter

math-ph2022

Surgery transformations and spectral estimates of $δ$ beam operators

Aftab Ali, Muhammad Usman

We introduce $δ$ type vertex conditions for beam operators, the fourth derivative operator, on metric graphs and study the effect of certain geometrical alterations (graph surgery)…

math-ph2022

Surgery transformations and eigenvalue estimates for quantum graphs with $δ^{'}$ vertex interactions

Aftab Ali, Muhammad Usman

We extend the surgical tool box for quantum graphs to anti-standard and $δ^{'}$ vertex conditions. Monotonicity properties of eigenvalues of graph Laplacian with $δ^{'}$ interactions at…

Surgery transformations and spectral estimates of δ beam operators

Surgery transformations and eigenvalue estimates for quantum graphs with δ′ vertex interactions

Surgery transformations and spectral estimates of $δ$ beam operators

Surgery transformations and eigenvalue estimates for quantum graphs with $δ^{'}$ vertex interactions