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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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  • $\begingroup$ Context would help here. Where was it? $\endgroup$ May 26, 2013 at 17:49
  • $\begingroup$ University professor's lectures on operator algebras. $\endgroup$
    – haijo
    May 26, 2013 at 18:01
  • $\begingroup$ As you see from Robert Israels guesses, it is still unclear. Why don't you ask the professor? $\endgroup$ May 27, 2013 at 7:24

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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).

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