Linearized Boltzmann collision operator: II. Polyatomic molecules modeled by a continuous internal energy variable

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding results mixtures polyatomic where polyatomicity modeled by discrete internal energy variable, are more recently obtained. In this work compactness species, which number degrees freedom greater or equal to two continuous studied. obtained proving that its terms are, or, at least, approximated by, Hilbert-Schmidt operators, under some assumptions on kernel. Self-adjointness follows. Moreover, bounds - including coercivity particular kernels hard sphere like models, but also potential with cut-off models. Then it follows Fredholm