V. Rybalko

Short scale asymptotics in nonlocal spectral problems

We study the asymptotic behavior of eigenvalues of nonlocal convolution-type operators $$L_\varepsilon\rho=-\frac{1}{\varepsilon^{d}}\int_\Omega J\left({\frac{|x-y|^2}{\varepsilon^2}}\right)\rho(y)dy+a(x)\rho(x),$$ (with a continuous sufficiently fast decaying at infinity function $J\geq 0$) when the scaling parameter...