Sentence examples for spectral measure from inspiring English sources

The familiar quantum measurement axiom that the distribution of the result of the "measurement of the observable A" is given by the spectral measure for A relative to the wave function (in the very simplest cases just the absolute squares of the so-called probability amplitudes) is thus obtained.

Consider the spectral measure (E_2).

where Φη (dλ), F η (dλ), f η representative the random spectral measure, spectral measure and broad spectral measure of η(t).

Let the random spectral measure of X t) is Φ X (dλ), and the spectral measure is F X (dλ), the broad spectral measure which also named the spectral measure of absolutely continuous part of F is f X.

part of the spectral measure for the vector δ1.

Let X t), t ∈ R is stationary processes, F (dλ) and Z(dλ) are spectral measure and random spectral measure respectively.

Let E be a spectral measure and (Phi in mathfrak {M}(E,E)).

It has been conjectured that a frame-spectral measure must be translationally absolutely continuous, which is a criterion describing the local uniformity of a measure on its support.

A finite Borel measure μ in Rd is called a frame-spectral measure if it admits an exponential frame (or Fourier frame) for L2.

If (dnu ) is the H-spectral measure for (A^*varphi ), then (14.6) says that begin{aligned} nu (I) le ||A||_H ||varphi ||^2 |I| end{aligned} (14.9)(where (|cdot |) is Lebesgue measure) for open intervals, I.

There is a corresponding decomposition ({mathcal H}= {mathcal H}_{ac}(H oplus {mathcal H}_{sc}(H oplus {mathcal H}_{pp}(H)) where ({mathcal H}_{y}) is the set of those vectors, (varphi ), whose H-spectral measure is purely of type y.