Preprint of the project: DFG research group "Spectral analysis, asymptotic distributions and stochastic dynamics"Numerical approximation and spectral analysis of infinite-dimensional dynamical systems04-045 Vasiliy S. Kolezhuk. In the study of parabolic differential equations on the real line and their discretizations, various weighted Sobolev spaces appear. In this paper, we establish some relations between these spaces. The main applications of these relations are in the study of convergence of discretized attractors towards exact ones.
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