A recurring task in image processing, approximation theory, and the numerical solution of partial differential equations is to reconstruct a piecewise-smooth real-valued function f(x), where x ∈ R , from its truncated Fourier transform (its truncated spectrum). An essential step is edge detection for which a variety of one-dimensional schemes have been developed over the last few decades. Most ...

Zamolodchikov's c-theorem is reformulated by using the spectral representation for the two-point function of the stress tensor . This approach makes explicit the unitarity constraints on the field theory and implements a nice physical picture of the renormalization group flow . An attempt is made to generalize the theorem above two space-time dimensions . There are two candidate c-functions, th...

Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures a class Schr\"odinger operators in bounded intervals.

We describe the concept of a super compact diffractive imaging spectrometer, with optical components a few millimeters across in all dimensions, capable of detecting optical fluorescence spectra within the entire visible spectral range from 400 nm to 700 nm with resolution of the order of 2 nm. In addition, the proposed spectrometer is capable of working simultaneously with multiple, up to 35, ...

Sparse trees are trees with sparse branchings. The Laplacian on some of these trees can be shown to have singular spectral measures. We focus on a simple family of sparse trees for which the dimensions can be naturally defined and shown to be finite. Generically, this family has singular spectral measures and eigenvalues that are dense in some interval.