Feb 28, 2008 · A "function space" is a vector space in which the "vectors" are functions. You often see the simplest examples, "the set of all polynomials of degree less than or equal to 3", say, in Linear …

Oct 26, 2017 · A "function space" is simply a set of functions from a given set to another given set. There isn't anything particularly important about the term "space," although most function spaces of …

Jan 31, 2021 · In a Hilbert space the linear combination can contain an infinite number of terms, and the sum of the infinite sum is defined through the norm induced by the inner product. The elements in a …

Jan 25, 2014 · The term "function space" is not a precise mathematical term like "Hilbert space" or "Banach space". It is merely an indication that we have a vector space and we are inclined (at least …

May 5, 2016 · 3 So the whole space of functions from $\mathbb {R}$ to $\mathbb {R}$ really does contain "uncountable vectors". But we usually deal with much smaller subspaces of that (in the …

Aug 28, 2017 · Function Space and Subspace Ask Question Asked 8 years, 8 months ago Modified 8 years, 8 months ago

Mar 28, 2015 · I am confused by the notion of a function space. For example consider the basis $\\{1, x, x^2\\}$ which is the basis for the vector space of all polynomials of degree at most $2$. What is the …

In spatial euclidean vector spaces norm is an intuitive concept: It measures the distance from the null vector and from other vectors. The generalization to function spaces is quite a mental leap ...

I am struggling to understand what the space $L^1$ is, and what it means for a function to be $L^1$. A friend told me that a function $f$ is $L^1$ if $\int_\mathbb {R} |f|$ is finite.

Feb 20, 2022 · The norm is something that is defined on top of the function space for use in proofs and so on. Kind of like $\mathbb {R}^2$ is just the space of ordered pairs of real numbers.