SPECTRAL DIMENSIONS OF KREĬN-FELLER OPERATORS AND Lq-SPECTRA

The paper’s Theorem 1.1 proves the exact chain F_ν ≤ h_m_ν ≤ s_ν ≤ h_ν ≤ h^ν = h^m_ν = s^ν = q^ν = F^ν for 1 < m ≤ 3, the bound q^ν ≤ 1/2, and the two equivalence criteria for the existence of the spectral dimension. The candidate solution reproduces the same structure: Dirichlet/Neumann bracketing, Poincaré-type lower bounds, entropy partitions, dyadic packing, and the identification with the L^q fixed point and coarse multifractal exponents. One minor slip is an inverted constant in the one-interval eigenvalue estimate (they wrote (m−1)/4 instead of 4/(m−1)), but they then use the correct threshold 4/(x(m−1)) and so their bracketing conclusions remain valid. Aside from that typographical constant issue and a harmless “up to constant” bound where the paper proves an exact inequality, the approach and conclusions agree with the paper.