Densities and summability

Absolute continuity and summability of transport densities: simpler proofs and new estimates

The paper presents some short proofs for transport density absolute continuity and L estimates. Most of the previously existing results which were proven by geometric arguments are re-proved through a strategy based on displacement interpolation and on approximation by discrete measures; some of them are partially extended.

Abel summability and angular convergence

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

Summability in topological spaces

On statistical A-summability

Let A = (ank)∞n,k=1 be an infinite matrix and x = (xk) ∞ k=1 a sequence of real or complex numbers. Then the A-transform of x is a sequence Ax = (An(x))where An(x) = ∑ ∞ k=1 ankxk provided that the series converges for each n; and the sequence x is said to be A-summable if Ax is convergent. In this paper we define statistical A-summability of x, that is, x is said to be statistically A-summable...

Densities, spectral densities and modality

This paper considers the problem of specifying a simple approximating density function for a given data set (x1, . . . , xn). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the l...