6533b839fe1ef96bd12a599f

RESEARCH PRODUCT

Generators of Random Processes in Ultrametric Spaces and Their Spectra

Witold Karwowski

subject

CombinatoricsClass (set theory)Square-integrable functionStochastic processStructure (category theory)Space (mathematics)Ultrametric spaceUnitary stateSpectral lineMathematics

description

The L 2(\( \mathbb{S} \)) space of square integrable functions on an ultrametric space \( \mathbb{S} \) has rather specific structure. As a consequence in a natural way there appear in L 2(\( \mathbb{S} \)) the operators of which unitary counterparts in L 2(ℝn) would be difficult to construct. Such class of self-adjoint operators emerge from theory of random processes on ultrametric spaces. In this paper we collect known material on spectral properties of the generators of random processes on \( \mathbb{S}_B \) an ultrametric space of sequences. (The set of p-adic numbers is a subset of \( \mathbb{S}_B \).) Then we discuss structure of the eigenspaces of the generators.

yearjournalcountryeditionlanguage
2009-01-01
https://doi.org/10.1007/978-3-7643-9919-1_22