# Operator valued distribution

1. Dec 26, 2009

### jostpuur

How precisely are operator valued distributions defined?

2. Dec 27, 2009

### Fredrik

Staff Emeritus
Isn't it defined exactly the same as a real-valued or complex-valued distribution, except that it takes values in the set of linear operators on a Hilbert space? See also posts #34 and #35 in this thread (option 2 only, since you convinced me option 1 doesn't work, as acknowledged in #43).

Hm, maybe I should have said "the set of bounded linear operators"...not sure about that.

There's probably an exact definition in Streater & Wightman. That's the first place I'd look for one.

3. Dec 27, 2009

### DarMM

An operator valued distribution is a continuous linear map from the space of test functions to the space of operators over a Hilbert space. Quantum fields are operator valued distributions which have a Fourier transform.