Philip Lilien

Directional Probe Energy in Banded Fractional Hessians Fractional stiffness, angular completeness, spectral mixing, and the geometric-coercivity problem

We introduce a banded fractional-Hessian framework for measuring the scale-dependent energy of tube-localized directional probes. For an -normalized probe concentrated in a unit-length tube of transverse radius , a band with fractional stiffness index contributes energy of order...

Directional Probe Energy in Banded Fractional Hessians Fractional stiffness, angular completeness, spectral mixing, and the geometric-coercivity problem

We introduce a banded fractional-Hessian framework for measuring the scale-dependent energy of tube-localized directional probes. For an -normalized probe concentrated in a unit-length tube of transverse radius , a band with fractional stiffness index contributes energy of order...