Some types of lacunary Fourier series

Analytic and arithmetic properties of thin sets

“…contrary to the definition of κ(E). Hence E contains no such difference of an alternating pair of size M. It follows easily from this property of E that E U Z~ satisfies condition FP 3 . This accounts for the part of Corollary 1 concerning t/C-sets, because, in discussing properties of E U Z" one may assume that E C Z 4 ".…”

On some properties of the class of stationary sets

“…(see for example [1] or [3]). Obviously, Λ is a p-Sidon set implies Λ is a q-Sidon set for q > p. If Λ is a p-Sidon set and not a q-Sidon set for any q < p, Λ is called a true p-Sidon set.…”

On lacunary sets for nonabelian groups

“…For typographical and historical reasons, I have preferred to alter the notation of Bozejko and Pytlik (1972 …”

“…Closer examination of Bozejko and Pytlik (1972) shows that many of the results therein (in particular Theorems 1 and 2) have straightforward generalizations to the non-abelian case-I summarize these in Section 3. Section 4 is devoted to central and local central analogues of these sets (cf.…”

“…But the results have been disappointing; many well-behaved non-abelian groups, even compact connected Lie groups, can fail to have infinite central Sidon sets in their dual object (Price, 1971;Rider, 1972). Bozejko and Pytlik (1972), in the case of an abelian group, provided a unifying concept for lacunary sets (their sets of type S p g and S% tQ include most types of lacunary sets previously considered) and at the same time introduced some a priori new families of lacunary sets. Edwards and Ross (1974) show that some of their families are strictly larger than previously known famines of lacunary sets, but only for the abelian case.…”