Gelfand–Shilov space
Encyclopedia
In the mathematical field of functional analysis
, a Gelfand–Shilov space S is a space of test functions for the theory of generalized function
s, introduced by .
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, a Gelfand–Shilov space S is a space of test functions for the theory of generalized function
Generalized function
In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognized theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing physical phenomena such as point charges...
s, introduced by .