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: http://lib.mexmat.ru/books/100051
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Дата индексирования: Tue Apr 12 15:25:19 2016
Кодировка: Windows-1251
Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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Название: Collision Operators as Generators of Markov Processes and Their Spectra
Авторы: Illner R., Kuscer I.
Аннотация:
The Markovian description of diffusion in velocity space involves a semigroup, which because of detailed balance is conveniently interpreted in a weightedL 2-space. The collision operatorC, defined by the corresponding generator, is positive semidefinite in this space. For a jump process and a continuous process we obtain the collision operators of the linear Boltzmann and Fokker-PIanck equations, respectively. If in the latter case the friction tensor has a nonvanishing limit as , the spectrum ofC is discrete. The Fourier-transformed transport operatorT k=C+ikћv is studied as a holomorphic family of sectorial operators. In the stated Fokker-Planck example, the spectrum ofT k remains discrete for arbitrary k.