TY - CHAP

T1 - Duality and Distributions

T2 - An Application of Topological Vector Spaces

AU - Lützen, Jesper

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - The theory of generalized functions called distributions has a two-fold origin: The problems that created a desire for a generalization of the concept of functions came from classical hard analysis; the methods that provided the solution came from modern structuralist functional analysis. According to the main proponent of the latter, Bourbaki (1960 and 1955), the development of the theory of normed spaces came to a temporary halt after the appearance of Stefan Banach’s book Théorie des opérations linéaires (1932). Instead, functional analysis went in the direction of more general spaces such as locally convex spaces in particular Frechet spaces.

AB - The theory of generalized functions called distributions has a two-fold origin: The problems that created a desire for a generalization of the concept of functions came from classical hard analysis; the methods that provided the solution came from modern structuralist functional analysis. According to the main proponent of the latter, Bourbaki (1960 and 1955), the development of the theory of normed spaces came to a temporary halt after the appearance of Stefan Banach’s book Théorie des opérations linéaires (1932). Instead, functional analysis went in the direction of more general spaces such as locally convex spaces in particular Frechet spaces.

U2 - 10.1007/978-3-031-59797-8_15

DO - 10.1007/978-3-031-59797-8_15

M3 - Book chapter

AN - SCOPUS:85200465289

SN - 978-3-031-59796-1

T3 - Science Networks. Historical Studies

SP - 717

EP - 730

BT - Duality in 19th and 20th Century Mathematical Thinking

PB - Springer

ER -