Once I met a notation of "spectral decomposition function" (for a selfadjoint operator). No definition was given. Could someone give me a clue what can that be, cause I can't find this exact phrase anywhere. Thank you!
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My guess is that this is referring to the resolution of the identity corresponding to the operator, which is sometimes called the "spectral decomposition" (e.g. in Rudin, Functional Analysis) or "spectral function" (e.g. in Akhiezer and Glazman, Theory of Linear Operators in Hilbert Space). 

