Corrigendum to “Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions” [J. Math. Anal. Appl. 517 (1) (2023) 126579] (Journal of Mathematical Analysis and Applications (2023) 517(1), (S0022247X22005935), (10.1016/j.jmaa.2022.126579))

We correct an inexactly-stated assumption in our paper [2] entitled “Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions” and published in Journal of Mathematical Analysis and Applications (DOI: 10.1016/j.jmaa.2022.126579). We highlight that, once this assumption is taken into account, the proofs and results of our article are correct. The assumption modification only impacts the understanding on which type of cross-sections can be considered. In [2], we considered a cross-section B depending on [Formula presented]. We assumed B to satisfy the following symmetry and micro-reversibility conditions: for almost every v, [Formula presented], I, [Formula presented], [Formula presented] and σ, [Formula presented] [Formula presented] We then defined, for suitable nonnegative functions f defined on [Formula presented], the Boltzmann operator Q as [Formula presented] where μ is an admissible measure on [Formula presented], i.e. such that there is an almost-everywhere positive function φ on [Formula presented] such that [Formula presented] which behaves like power laws around 0 and infinity (see [2, Equations (2.1)–(2.2)]). However, under assumption (1.2), the measure [Formula presented] is not reversible, in the sense that it is not invariant by the change of variable [Formula presented] We replace the micro-reversibility assumption (1.2) (corresponding to [2, Equation (2.12)]) by the following assumption [Formula presented] Then, under (1.4), the measure [Formula presented] is indeed reversible, in the sense that it is invariant by the change of variable [Formula presented] No other changes are needed throughout the paper. The modification of the reversibility assumption of B has no other impact on the result than on the clarity of which cross-sections can be considered: indeed, (1.4) is less clear and less standard than (1.2). To provide a clearer view on which cross-sections can actually be considered, one shall indeed consider assumption (1.2), with however a variant definition of the Boltzmann operator than (1.3), which would read [Formula presented] One shall verify that, when (1.2) is in force, the measure [Formula presented] is indeed reversible, see [1, Chapters 4 and 5] for more details on this matter. The authors would like to apologize for any inconvenience caused.