A bounded function φ : G → C on an LCA group G is called Hartman measurable if it can be extended to a Riemann integrable function φ∗ : X → C on some group compactification (ιX , X), i.e. on a compact group X such that ιX : G → X is a continuous homomorphism with image ιX(G) dense in X and φ = φ ∗ ◦ ιX . The concept of Hartman measurability of functions is a generalization of Hartman measurabil...

In recent papers the concept of Hartman (measurable) sets was investigated. A subset H of the integers, or more generally, of a topological group G is called Hartman measurable (or simply a Hartman set), if H = ι(M) for some continuous homomorphism ι : G → C, C = ι(G) a compact group, and M ⊆ C a set whose topological boundary ∂M is a null set w.r.t. the Haar measure on C. This concept turned o...

The Hartman–Grobman Theorem (see [3, page 353]) was proved by Philip Hartman in 1960 [5]. It had been announced byGrobman in 1959 [1], likely unbeknownst to Hartman, and Grobmanpublished his proof in 1962 [2], likely without knowing of Hartman’s work. (Grobman attributes the question to Nemycki and an earlier partial result to R.M. Minc (citing Nauč. Dokl. Vysš. Školy. Fiz.-Mat. Nauki 1 (1958))...

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...

The disconjugacy theory for forward difference equations was developed by Hartman [15] in a landmark paper which has generated so much activity in the study of difference equations. Sturm theory for a second-order finite difference equation goes back to Fort [12], which also serves as an excellent reference for the calculus of finite differences. Hartman considers the nth-order linear finite di...

It is indeed a great honor to be selected by the Society to receive the Hartman Award and I am most grateful. 1 was an ardent admirer of Carl Hartman from the time I first met him in the early ‘40’s at Stanford University. He was a personal friend of Joe Markee with whom I worked and whom 1 accompanied to Duke University and I had the benefit of numerous discussions while Hartman was visiting M...