Suppose we have i.i.d. observations with a distribution equal to the convolution of an unknown distribution function F and a known distribution function K. We derive local minimax lower bounds for the problem of estimating F , its density f and its derivatives at a xed point x 0. Contrary to a previous local minimax bound in Van Es (1998) only smooth perturbations are considered. The local boun...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

We study the approximation properties of Runge-Kutta time discretizations of linear and semilinear parabolic equations, including incompressible Navier-Stokes equations. We derive asymptotically sharp error bounds and relate the temporal order of convergence, which is generally noninteger, to spatial regularity and the type of boundary conditions. The analysis relies on an interpretation of Run...

We study the orthogonal perturbation of various coherent function systems (Gabor systems, Wilson bases, and wavelets) under convolution operators. This problem is of key relevance in the design of modulation signal sets for digital communication over time–invariant channels. Upper and lower bounds on the orthogonal perturbation are formulated in terms of spectral spread and temporal support of ...

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution in-tegrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this descript...

A time-domain approach for distortion analysis of electromagnetic field senors is developed in Laguerre functions subspace. Using Laguerre convolution preservation property, it is proved that every electromagnetic field sensor corresponds to an equivalent discrete-time LTI system. The equivalent discrete-time system is compared to a reference system as a measure of distortion. Further, this ana...

We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. These results are compared with the corresponding ones ...

We derive a lower bound on the differential entropy of a log-concave random variable X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the rate-distortion function and the channel capacity. Specifically, we study the rate-distortion function for log-concave sources and distortion measure |x− x̂|,...

This thesis studies theoretical and practical aspects of the computation of planar polygonal Minkowski sums via convolution methods. In particular we prove the “Convolution Theorem”, which is fundamental to convolution based methods, for the case of simple polygons. To the best of our knowledge this is the first complete proof for this case. Moreover, we describe a complete, exact and efficient...