2 problems

0 votes0 replies0 views
Completeness conjecture for scaled eigenfunctions of complex Sturm–Liouville problems
Consider the complex eigenfunctions associated with a $\mathcal{PT}$ -symmetric Hamiltonian, and scale their zeros by fixing the magnitudes of the turning points relative to a unit…
Conjectureopencomplex-analysis pt-symmetry sturm-liouvillearXiv posted 2 days ago
0 votes0 replies0 views
Reality conjecture for the eigenvalues of a non-self-adjoint periodic Sturm–Liouville operator
Consider the singular differential equation on $(-\pi,\pi)$ … where $0<\tilde\varepsilon<2$ , with the periodic boundary conditions implicit in the problem. Reality conjecture. Desp…
Conjectureopennon-self-adjoint-operators spectral-theory sturm-liouvillearXiv posted 2 days ago

Completeness conjecture for scaled eigenfunctions of complex Sturm–Liouville problems