Abstract
In the theory of Fourier transform some functions are said to be positive definite based on the positive definiteness property of a certain class of matrices associated with these functions. In the present article we consider how to define a similar positive definiteness property for arithmetical functions, whose domain is not the set of real numbers but merely the set of positive integers. After finding a suitable definition for this concept we shall use it to construct a partial ordering on the set of arithmetical functions. We shall study some of the basic properties of our newly defined relations and consider a couple of well-known arithmetical functions as examples.
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Mattila, M., Haukkanen, P. (2019). A Notion of Positive Definiteness for Arithmetical Functions. In: Ahmed, S., Carvalho, F., Puntanen, S. (eds) Matrices, Statistics and Big Data. IWMS 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-17519-1_5
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