# spectral measure

how to calculate spectral measure for a given normal operator for example right shift operator?

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This looks like a homework problem, so don't be surprised if your question is closed - see the faq. You'll find a lot of information on how to calculate certain parts of the spectrum of certain operators in the book Reed/Simon: "Methods of Modern Mathematical Physics", Volume 4: "Analysis of Operators". – Tim van Beek Feb 6 '11 at 16:39

The spectral decomposition for the unbd. operator $-i d/dx$ can be computed from that of a multiplication operator via the Fourier-Plancherel transform. That's in Kato's book on functional analysis.
Another way is to compute first of all the polynomial calculus for your operator $T$, which sometimes is doable and then make a guess about how $f(T)$ looks like for say continuous functions f (of course you must then find a proof and show that if polynomials $p_n$ tend to $f$, then $p_n(T)$ goes to $f(t)$. If you send me an email, I can send you some examples.