O'Reilly logo

Advanced Mathematics for Applications by Andrea Prosperetti

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Theorem 21.11.3 Let Eλ be a resolution of the identity in a Hilbert space H . The family Eλ defines a self-adjoint operator A in H with domain image consisting of all vectors u for which

image

(21.11.17)

The action of the operator A is uniquely defined by29

image

(21.11.18)

While the theorem is illuminating, its real power lies in the converse statement, namely that every self-adjoint operator can be represented in the form (21.11.18). With the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required