A complex exponential map is said to be Misiurewicz if the forward trajectory of the asymptotic value 0 lies in the Julia set and is bounded. We prove that the set of Misiurewicz parameters in the exponential family λ exp(z), λ ∈ C \ {0}, has Lebesgue measure zero.

The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct -by 1 norm minimization -a sparse quaternion signal from a limited number of its real linear measurements, provided the measurement matrix satisfies so-called restricted isometry property with a sufficiently small constant. We also provide error estimates for the reconstruction of a non-sparse quaternion signal in the noisy and noiseless cases. arXiv:1605.07985v1 [math.FA]

No abstract

We prove that for a hyperbolic meromorphic function f having a rapid derivative growth, if HD (J(f))>1, then the Jacobian Dμϕ of a probability invariant measure μϕ on J(f), equivalent to a conformal measure mϕ, has a real analytic extension on a neighbourhood of J(f)∖ f−1(∞) in ℂ. If, in addition, f satisfies a balanced derivative growth condition with constant exponents, then this extension is bounded in a neighbourhood of every pole of f.

No abstract