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The Wikipedia article on spectral decomposition, see here https://en.wikipedia.org/wiki/Self-adjoint_operator says the following: A self-adjoint operator A on $H$ has pure point spectrum if and ...

Suppose $D$ is the Dirac operator on a closed spin manifold $M$, with spinors $S$. One can take the functional calculus of $D$ with respect to the continuous function $f:\mathbb{R}\rightarrow\mathbb{R}...

Hi... I am wondering how 'eigenvalues' that don't lie in my Hilbert space combine into producing the spectral measure. I study probability and I am quite ignorant in the field of spectral analysis of ...

The following is well known. Given a symmetric differential operator, like $\partial_x^2$, defined on smooth functions of compact support on $\mathbb{R}$, $C_0^\infty(\mathbb{R})$, one can count the ...