Optimal fractional discrete Hardy inequalities on the half-line

What the math gives to ML

The paper proves a sharp coercivity inequality for a fractional discrete Laplacian compressed to a one-sided domain. Its transferable asset is a boundary-aware, position-dependent weight that is rigorously dominated by a nonlocal smoothness energy, with an explicit optimal Gamma-function constant for every fractional order. A practical neural-network adaptation is to regularize hidden-state sequences using the resulting nonnegative Hardy deficit, rather than applying an undifferentiated smoothness penalty that ignores sequence boundaries.