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- Title
A spectral study of the linearized Boltzmann operator in L<sup>2</sup>-spaces with polynomial and Gaussian weights.
- Authors
Gervais, Pierre
- Abstract
The spectrum structure of the linearized Boltzmann operator has been a subject of interest for over fifty years and has been inspected in the space by B. Nicolaenko [ 27 ] in the case of hard spheres, then generalized to hard and Maxwellian potentials by R. Ellis and M. Pinsky [ 13 ], and S. Ukai proved the existence of a spectral gap for large frequencies [ 33 ]. The aim of this paper is to extend to the spaces the spectral studies from [ 13 , 33 ]. More precisely, we look at the Fourier transform in the space variable of the inhomogeneous operator and consider the dual Fourier variable as a fixed parameter. We then perform a precise study of this operator for small frequencies (by seeing it as a perturbation of the homogeneous one) and also for large frequencies from spectral and semigroup point of views. Our approach is based on Kato's perturbation theory for linear operators [ 22 ] as well as enlargement arguments from [ 25 , 19 ].
- Subjects
POLYNOMIAL operators; PERTURBATION theory; OPERATOR theory; SPECTRAL theory; FOURIER transforms
- Publication
Kinetic & Related Models, 2021, Vol 14, Issue 4, p725
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2021022