Schrödinger means in higher dimensions
Maximal estimates for Schrödinger means and convergence almost everywhere of sequences of Schrödinger means are studied.
math.FA↗
arXiv subjects
Jan-Olov Strömberg
Publications and source records attributed to Jan-Olov Strömberg.
Analysis of Schrödinger means
We study integral estimates of maximal functions for Schrödinger means.
math.AP↗
On the Theorem of Uniform Recovery of Random Sampling Matrices
We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements (with high probability) is known to be $m\gtrsim s(\ln s)^3\ln N$. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of $m\times N$-matrices, by considering what we call \emph{low entropy}. We also present an improved condition on the so-called restricted isometry constants, $δ_s$, ensuring sparse recovery via $\ell^1$-minimization. We show that $δ_{2s}<4/\sqrt{41}$ is sufficient and that this can be improved further to almost allow for a sufficient condition of the type $δ_{2s}<2/3$.
cs.IT↗