Homogenization Algebras and Applications: A Deterministic Homogenization Theory

“Each chapter ends with comments and problems that give historical considerations and further examples or possible extensions. Throughout the whole book, the author takes great care to explain the arguments he develops and their purpose. … The proofs of the different results are easy to follow. There are numerous examples illustrating the power of the proposed tools … . The book will certainly help researchers interested in homogenization problems for elliptic or parabolic problems.” (Alain Brillard, Mathematical Reviews, April, 2026)

The book presents a deterministic homogenization theory intended for the mathematical analysis of non-stochastic multiscale problems, both within and beyond the periodic setting. The main tools are the so-called homogenization algebras, the classical Gelfand representation theory, and a class of actions by the multiplicative group of positive real numbers on numerical spaces. The basic approach is the Sigma-convergence method, which generalizes the well-known two-scale convergence procedure. Numerous problems are worked out to illustrate the theory and highlight its broad applicability. The book is primarily intended for researchers (including PhD students) and lecturers interested in periodic as well as non-periodic homogenization theory.