On positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs Measures
Abstract
From \cite{re} From \cite{re} it is known that ``translation-invariant Gibbs measures" of the model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. In \cite{enh2015, MSSX} there are main results on positive fixed points of the operator of Hammerstein type with degenerate kernels, but it was not solved the existence of Gibbs measures corresponding to the founded fixed points for constructed kernels. This paper is an investigation of the papers \cite{enh2015} and \cite{MSSX}. In this paper we construct new degenerate kernels of the Hammerstein operator by taking into account problems in the theory of Gibbs measure, i.e. each positive fixed point of the operator gives translational-invariant Gibbs measure.
Keywords
Cite
@article{arxiv.2306.08496,
title = {On positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs Measures},
author = {I. M. Mavlonov and Kh. N. Khushvaktov and G. P. Arzikulov and F. H. Haydarov},
journal= {arXiv preprint arXiv:2306.08496},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2305.15443