id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-10553	Exner, Pavel	Quantum graphs featuring unusual self-adjoint extensions	2025	7	.pdf	application/pdf	5379	296	68	By Krein’s formula [9] the resolvents of Ĥ and HD differ by an operator of rank not exceeding N (in fact, equal to N − 1), hence their essential spectra coincide and we get σess(Ĥ) = ∅. Furthermore, both Ĥ and HD are self-adjoint exten- sions of the same symmetric operator of the deficiency indices not exceeding N (the domain of which is ob- tained by imposing the conditions ψj(0) = ψ′ j(0) = eiθAout j (V ψ) at infinity; one is Neumann at the origin and N − 1 satisfy Dirichlet condition there.	cache/ap-10553.pdf	txt/ap-10553.txt