A viscoelastic modulus admits an exact finite Prony series if and only if its Mellin kernel pole lattices align arithmetically with the constitutive integer lattice and residues satisfy decoupled first-order recurrences.
Bernstein, Sur les fonctions absolument monotones, Acta Mathematica 52 (0) (1929) 1–66
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Establishes optimal constants and extremizers for smoothing estimates of quantum harmonic oscillators as direct analogues of prior free-particle results.
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Mellin-Space Prony Representability of Linear Viscoelastic Models
A viscoelastic modulus admits an exact finite Prony series if and only if its Mellin kernel pole lattices align arithmetically with the constitutive integer lattice and residues satisfy decoupled first-order recurrences.