Brief communications

On Gaussian self-similar random fields on a 2-adic plane

M. D. Missarov

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar random fields). Fields are characterized by quadratic characteristic functionals defined by homogeneous generalized functions on a 2-adic space. The properties of the proposed generalized homogeneous functions are investigated and the positive definiteness of the correlation functionals is proved.

Keywords: Gaussian field, $p$-adic space, scaling transformation, characteristic functional, homo-geneous generalized function.

UDC: 519.21

Received: 20.03.2020
Revised: 20.03.2020
Accepted: 25.03.2020

DOI: 10.26907/0021-3446-2020-5-94-99

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:5, 83–87

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