An Operator-Fractal

Mathematics – Operator Algebras

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

25 pages

Scientific paper

Certain Bernoulli convolution measures (\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be spectral, the orthonormal basis need not be unique; indeed, there are often families of such spectral bases. Let \lambda = 1/(2n) for a natural number n and consider the Bernoulli measure (\mu) with scale factor \lambda. It is known that L^2(\mu) has a Fourier basis. We first show that there are Cuntz operators acting on this Hilbert space which create an orthogonal decomposition, thereby offering powerful algorithms for computations for Fourier expansions. When L^2(\mu) has more than one Fourier basis, there are natural unitary operators U, indexed by a subset of odd scaling factors p; each U is defined by mapping one ONB to another. We show that the unitary operator U can also be orthogonally decomposed according to the Cuntz relations. Moreover, this operator-fractal U exhibits its own self-similarity.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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 An Operator-Fractal, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Operator-Fractal will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-570369

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.