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The hat superscript implies that the function depends in time on t and τ, as opposed to t1 and t2, or in frequency on ω and ω as opposed to ω1 and ω2. However, for functions of only a single variable t or τ, or ω or ω, the symbol is not used.
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19
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note
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Since Γ(t1, t2) has to remain finite, the Dirac delta function δ(t2-t1) is to be interpreted as a limiting case of a narrow function with a very high but normalizable value.
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