Cora Calvo, VictorFernández Fernández, Francisco JavierFernández Tojo, Fernando Adrián2023-05-302023-05-302023Journal of Mathematical Analysis and Applications 526 (2023) 127259http://hdl.handle.net/10347/30621In this work we develop a theory of Stieltjes-analytic functions. We first define the Stieltjes monomials and polynomials and we study them exhaustively. Then, we introduce the g-analytic functions locally, as an infinite series of these Stieltjes monomials and we study their properties in depth and how they relate to higher order Stieltjes differentiation. We define the exponential series and prove that it solves the first order linear problem. Finally, we apply the theory to solve higher order linear homogeneous Stieltjes differential equations with constant coefficientseng© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)http://creativecommons.org/licenses/by-nc-nd/4.0/Stieltjes derivativeAnalytic functionsHigher order linear differential equationsExponentialStieltjes polynomialsjournal article10.1016/j.jmaa.2023.1272590022-247Xopen access