Duality and Distributions: An Application of Topological Vector Spaces
Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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Duality and Distributions : An Application of Topological Vector Spaces. / Lützen, Jesper.
Duality in 19th and 20th Century Mathematical Thinking. Springer, 2024. p. 717-730 (Science Networks. Historical Studies, Vol. 63).Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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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 -
ID: 402878643