# Type 1 and 2 sets for series of translates of functions

## Buczolich, Z. ✉ [Buczolich, Zoltán (Klasszikus analízis), szerző] Analízis Tanszék (ELTE / TTK / Mat_I); Hanson, B.; Maga, B. [Maga, Balázs (Matematika), szerző] Analízis Tanszék (ELTE / TTK / Mat_I); Vertesy, G.

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
Megjelent: ACTA MATHEMATICA HUNGARICA 0236-5294 1588-2632 158 (2) pp. 271-293 2019
• SJR Scopus - Mathematics (miscellaneous): Q2
Azonosítók
Szakterületek:
Suppose Lambda is a discrete infinite set of nonnegative real numbers. We say that Lambda is type 1 if the series s(x)=Sigma lambda is an element of Lambda f(x+lambda) satisfies a zero-one law. This means that for any non-negative measurable f:R ->[0,+infinity) either the convergence set C(f,Lambda)={x:s(x)<+infinity}=R modulo sets of Lebesgue zero, or its complement the divergence set D(f,Lambda)={x:s(x)=+infinity}=R modulo sets of measure zero. If Lambda is not type 1 we say that Lambda is type 2.The exact characterization of type 1 and type 2 sets is not known. In this paper we continue our study of the properties of type 1 and 2 sets. We discuss sub and supersets of type 1 and 2 sets and give a complete and simple characterization of a subclass of dyadic type 1 sets. We discuss the existence of type 1 sets containing infinitely many elements independent over the rationals. Finally, we consider unions and Minkowski sums of type 1 and 2 sets.
Hivatkozás stílusok:
2021-06-21 11:34