Conclusion

Abstract

AbstractKrull-Webster’s theory offered an elegant extension of Bohr-Mollerup’s theorem and has proved to be a very nice and useful contribution to the resolution of the difference equation Δf = g on the real half-line $$\mathbb {R}_+$$ ℝ + . In this book, we have provided a significant generalization of Krull-Webster’s theory by considerably relaxing the asymptotic condition imposed on the function g, and we have demonstrated through various examples how this generalization provides a unified framework to investigate the properties of many functions. This framework has indeed enabled us to derive several general formulas that now constitute a powerful toolbox and even a genuine Swiss Army knife to investigate a large variety of functions.