Suppose a discrete-time signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discrete-time signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time/frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the `1 norm of the coe cients among all decompositions. Here \highly sparse " means that Nt + Nw < p N=2 where Nt is the number of time atoms, Nw is the number of frequency atoms, and N is the length of the discrete-time signal.

In this paper I am careful to distinguish between the space of signals and the space of their Fourier transforms. Folland and Sitaram [4] give a survey of uncertainty principles in analysis. First we will go through the talk by Emmanuel Candès and Terence Tao, “The uniform uncertainty principle

-understandings are significant and telling of important and long-standing differences between feminist and other approaches in science studies. Pinch delivers his answer to the question of the relationship between science and sci-ence studies in the form of an ‘uncertainty principle’. As someone who studied quantum physics

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this paper is as follows. Suppose that is a superposition of spikes @ Aa @ A @ A obeying @�� � A I for some constant H. We do not know the locations of the spikes nor their amplitudes. Then with probability at least I @ A, can be reconstructed exactly as the solution to the I minimization problem I aH @ A s.t. ” @ Aa ” @ A for all

Black hole thermodynamics with generalized

the q-Dunkl Transform

for relatively dense sets and lacunary spectra

for arithmetic sequences

ABSTRACT. An uncertainty principle is obtained for a modified Yν-transform of order ν. The principle is similar to the classical Heisenberg-Weyl uncertainty principle for the Fourier transform on R.

The Uncertainty Principle (UP) as understood in this lecture is the following informal assertion: a non-zero “object” (a function, distribution, hyperfunc-tion) and its Fourier image cannot be too small simultaneously. “The smallness” is understood in a very broad sense meaning fast decay (at