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This article is cited in 57 scientific papers (total in 57 papers)
Wick and anti-Wick operator symbols
F. A. Berezin
Abstract:
In this paper Wick and anti-Wick operator symbols are studied in connection with expansion into normal and antinormal series in terms of generation and annihilation operators. By the aid of the Wick $A(\bar z,z)$ and anti-Wick $\overset0A(z,\bar z)$ symbol of the operator $\widehat A$ a series of characteristic spectral properties are identified for $\widehat A$. In particular,
results are presented concerning necessary and sufficient conditions (separately) for $\widehat A$ to belong to the classes of bounded operators, completely continuous operators and nuclear operators, and also concerning bounds on the spectrum of $\widehat A$, and the asymptotic behavior of the number $N(E)$ of eigenvalues below $E$; and for positive selfadjoint operators
a bound is obtained for the trace of the Green function:
$$
\int\exp\bigl[-tA(\bar z,z)\bigr]\Pi\,dz\,d\bar z\leqslant\operatorname{sp}\exp(-t\widehat A)\leqslant\int\exp\bigl[-tA(z,\bar z)\bigr]\Pi\,dz\,d\bar z.
$$
Bibliography: 14 titles.
Received: 23.12.1970
Citation:
F. A. Berezin, “Wick and anti-Wick operator symbols”, Math. USSR-Sb., 15:4 (1971), 577–606
Linking options:
https://www.mathnet.ru/eng/sm3319https://doi.org/10.1070/SM1971v015n04ABEH001564 https://www.mathnet.ru/eng/sm/v128/i4/p578
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Abstract page: | 933 | Russian version PDF: | 363 | English version PDF: | 49 | References: | 85 |
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