Mathematics – Spectral Theory
Scientific paper
2012-04-23
Mathematics
Spectral Theory
Scientific paper
We examine the operator $U_5$ defined on $L^2(\mu_{\frac14})$ where $\mu_{\frac14}$ is the 1/4 Cantor measure. The operator $U_5$ scales the elements of the canonical exponential spectrum for $L^2(\mu_{\frac14})$ by 5 --- that is, $Ue_{\gamma} = e_{5\gamma}$ where $e_{\gamma}(t) = e^{2\pi i \gamma t}$. It is known that $U_5$ has a self-similar structure, which makes its spectrum, which is currently unknown, of particular interest. In order to better understand the spectrum of $U_5$, we demonstrate a decomposition of the projection valued measures and scalar spectral measures associated with $U_5$. We are also able to compute associated Radon-Nikodym derivatives between the scalar measures. Our decomposition utilizes a system of operators which form a representation of the Cuntz algebra $\mathcal{O}_2$.
Jorgensen Palle E. T.
Kornelson Keri A.
Shuman Karen L.
No associations
LandOfFree
Scalar spectral measures associated with an Operator-Fractal does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Scalar spectral measures associated with an Operator-Fractal, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scalar spectral measures associated with an Operator-Fractal will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-444735