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Once I met a notation of "spectral decomposition function" (for a self-adjoint 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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closed as no longer relevant by Scott Morrison Jun 17 '13 at 2:49

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Context would help here. Where was it? –  András Bátkai May 26 '13 at 17:49
    
University professor's lectures on operator algebras. –  Usmi May 26 '13 at 18:01
    
As you see from Robert Israels guesses, it is still unclear. Why don't you ask the professor? –  András Bátkai May 27 '13 at 7:24

1 Answer 1

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).

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