This monograph investigates the deep, structural relationship between locally convex spaces and the theory of linear partial differential equations (PDEs). Trèves demonstrates how abstract functional analysis—specifically the duality theory of topological vector spaces—provides the necessary framework to solve fundamental problems in PDEs, such as existence, approximation, and regularity o…
This foundational monograph provides a rigorous and systematic exposition of the three subjects mentioned in its title, which are central to modern functional analysis and partial differential equations. Trèves develops the theory of topological vector spaces with a focus on their applications to the study of distributions (generalized functions). A major highlight is the treatment of the kern…