On a certain class of $g$-functions for subshifts

TL;DR

This paper explores a class of partially defined continuous g-functions for subshifts with property (D), extending the theory beyond finite type subshifts.

Contribution

It introduces and analyzes a new class of g-functions for subshifts with property (D), broadening the understanding of g-functions beyond finite type cases.

Findings

Characterization of property (D) subshifts with g-functions

Extension of g-function theory beyond finite type subshifts

Identification of conditions for partially defined continuous g-functions

Abstract

A property $(D)$ of subshifts was defined in: Wolfgang Krieger, On $g$-functions for subshifts, IMS Lecture Notes- Monograph Series, Vol. 48, Dynamics & Stochastics (2006) 306 - 316, arXiv:math.DS/0608259. With a view towards a theory of $g$-fnctions beyond the case of finte type subshifts partially defined continuous $g$-functions of property $(D)$ subshifts are studied.