TITLE: Self-adjoint operator
QUESTION [6 upvotes]: Assume that $B$ is a self-adjoint operator and $\alpha\in(0,1)$. I need a reference for the following equality $$B^{-\alpha}=\frac{\sin\alpha \pi}{\pi}\int_0^\infty \lambda^{-\alpha}(\lambda+B)^{-1}\mathrm d\lambda.$$

REPLY [3 votes]: See pp. 231-232 in Birman M.S., Solomyak M.Z. Spectral Theory of Self-Adjoint Operators in Hilbert Space (Reidel, 1987).