Multicriticality and Scaling: Mellin Spectral Theory, and the Decoupling of Geometric and Spectral Exponents

Laurence A. Jacobs, Alejandro Frank

We develop a spectral theory of scale-invariant operators on the multiplicative half-line $({\mathbb{R}}_{+},dx/x)$. A symmetric kernel $M(x,y)$ satisfying $M(kx, ky) = k^{-a}M(x, y)…