Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...122...39p&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 122, no. 1-2, June 1983, p. 39-44. Research supported by the Fonds National de
Astronomy and Astrophysics
Astrophysics
Stellar Gravitation, Stellar Models, Stellar Oscillations, Distribution Functions, Eigenvalues, Frequency Distribution
Scientific paper
The author establishes that for arbitrary stellar models the eigenvalues of the g-spectrum possess a set of limit points which is dense in at least some interval close to the frequency origin. In the framework of the homogeneous model he offers a mathematical proof that this set of limit points of the g-eigenvalues taken in modulus is dense in the whole positive half axis. This result implies that for the g-modes a frequency distribution function g(ω), conventionally defined as the number of g-frequencies per unit frequency interval, is everywhere infinite, and therefore ceases to be a sensible concept. It is shown that a meaningful relative distribution function for the g-modes can be defined, which is found to be identical with the relative density of the limit points of the g-spectrum.
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