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On the Essential Spectrum of a Differentially Rotating Star
Author(s) -
Faierman M.,
Lifschitz A.,
Mennicken R.,
Möller M.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199911)79:11<739::aid-zamm739>3.0.co;2-v
Subject(s) - star (game theory) , spectrum (functional analysis) , astronomy , astrophysics , physics , quantum mechanics
Natural oscillations of a differentially rotating star are governed by the linearized Euler equations. Separation of variables leads to a family k ,0 ( k ∈ ℤ) of mixed order partial differential operators. It is shown that for k ≠ 0 their closures k have nonempty essential spectrum. Indeed, it is shown that the essential spectrum of k coincides with the essential spectrum of a bounded operator. Some parts of the essential spectrum are calculated explicitly. It is still an open problem if there are more points in the essential spectrum.