In the limit \ beta \ to \ infty we obtain \ langle n \ rangle = | \ alpha | ^ 2, which is consistent with the expression for the density matrix operator at zero temperature.
12.
Duren received in 1956 his bachelor's degree from Harvard University and in 1960 his PhD from MIT under Gian-Carlo Rota with thesis " Spectral theory of a class of non-selfadjoint infinite matrix operators ".
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