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Haar system on a product of zero-dimensional compact groups

100%
Lukomskii S.
Open Mathematics
|
2011
|
tom 9
|
nr 3
627-639
EN
In this work, we study the problem of constructing Haar bases on a product of arbitrary compact zero-dimensional Abelian groups. A general scheme for the construction of Haar functions is given for arbitrary dimension. For dimension d=2, we describe all Haar functions.
2
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Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

72%
Cho I., Jorgensen P. E. T.
Special Matrices
|
2015
|
tom 3
|
nr 1
EN
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we consider free probability on AG.
3
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Matrices induced by arithmetic functions acting on certain Krein spaces

62%
Cho I.
Special Matrices
|
2017
|
tom 5
|
nr 1
258-289
EN
In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
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