标题: 【教程】function analysis [打印本页] 作者: OLS 时间: 2009-2-4 03:11 标题: 【教程】function analysis 本帖最后由 厚积薄发 于 2010-1-26 21:12 编辑 . Y0 j z7 _% O- K! E/ P7 C* J5 O0 R8 A
In mathematics, a functional is traditionally a map from a vector space to the field underlying the vector space, which is usually the real numbers. In other words, it is a function that takes a vector as its argument or input and returns a scalar. Its use goes back to the calculus of variations where one searches for a function which minimizes a certain functional. A particularly important application in physics is to search for a state of a system which minimizes the energy functional. . Q" q4 p8 V" E* ]. J* U0 @In functional analysis, the functional is also used in a broader sense as a mapping from an arbitrary vector space into the underlying scalar field (usually, real or complex numbers). A special kind of such functionals, linear functionals, gives rise to the study of dual spaces./ Z3 j2 n9 R0 S6 r
Transformations of functions is a somewhat more general concept, see operator.
