SPECTRAL MEASURES AND CUNTZ ALGEBRAS
Abbreviated Journal Title
Spectrum; Hilbert space; fractal; Fourier bases; selfsimilar; iterated; function system; operator algebras; COMPLEX HADAMARD-MATRICES; ITERATED FUNCTION SYSTEMS; LARGEST PRIME; FACTOR; MERSENNE NUMBERS; FRACTALS; REPRESENTATIONS; CONJECTURE; ISOMETRIES; OPERATORS; DIMENSION; Mathematics, Applied
We consider a family of measures p, supported in R-d and generated in the sense of Hutchinson by a finite family of affine transformations. It is known that interesting sub-families of these measures allow for an orthogonal basis in L-2(mu) consisting of complex exponentials, i.e., a Fourier basis corresponding to a discrete subset F in R-d. Here we offer two computational devices for understanding the interplay between the possibilities for such sets Gamma (spectrum) and the measures mu themselves. Our computations combine the following three tools: duality, discrete harmonic analysis, and dynamical systems based on representations of the Cuntz C*-algebras O-N.
Mathematics of Computation
"SPECTRAL MEASURES AND CUNTZ ALGEBRAS" (2012). Faculty Bibliography 2010s. 2513.