The central theme of this monograph is Khinchin-type representation theorems. An abstract
framework for unimodality, an example of applied functional analysis, is developed for the …

Let F be a distribution function and let Q F (l)=0 for l<0 and Q F (l)= sup {F(x+l)−F(x): x∈ℝ}
for l≧0 be its Lévy concentration function. This paper has two purposes: to give a …

Intuitively, a probability measure# on R is unimodal (at a) if its probability density f is single
humped. In [7], this notion is formalized by the condition that the distribution function F of/~ is …

SOME CHARACTERIZATIONS OF DISCRETE UNIMODALITY Page 1 Statistics & Probability
Letters 2 (1984) 23-30 North-Holland SOME CHARACTERIZATIONS OF DISCRETE …

Fonctions harmoniques non-reelles Page 1 MATHEMATICS FONCTIONS HARlYIONIQUES
NON-REELLES PAR E. M. J. BERTIN (Communicated by Prof. TA SPRINGER at the meeting …

Let X be a real-valued random variable, let μ be its probability distribution (or simply distribution)
on R, and let F be its (right continuous) distribution function. The variable X (or F or μ) is …

La theorie axiomatique des espaces harmoniques, comme d&rite par exemple dans
Constantinescu et Cornea [1972], eat une theor Page 1 MATEEMATIOS …

As we already mentioned, Khinchin’s classical unimodality on R is a special case of beta
unimodality on a Hilbert space H, obtained by taking α = v = 1 and H = R in Section 3.1. Further …

In Example 2.7.14 we showed that, in general, unimodality on R is not preserved by
convolution. The correction of this anomaly is the merit of Ibragimov [Ibr56], who introduced the …

In Chapter 2 we constructed and studied Khinchin spaces, our framework for unimodality. In
this chapter we examine (Section 3.1) a new concept of unimodality on a Hilbert space H, in …