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Course# MATH-404: Functional analysis II

Summary

We introduce locally convex vector spaces. As an example we treat the space of test functions and the space of distributions. In a second part of the course we discuss differential calculus in Banach spaces and some elements from nonlinear functional analysis.

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Related concepts (25)

Self-adjoint operator

In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle (equivalently, a Hermitian operator in the finite-d

Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the co

Normed vector space

In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in

Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological

Fréchet derivative

In mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single r

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