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Results tagged with fa.functional-analysis
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user 88133
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
Accepted
Cores in the tensor-train decomposition
Yes, mapping $A \otimes B \otimes C$ to $A \otimes C$ by choosing a coordinate of $B$ (equivalently, basis element of dual space $B^*$) is indeed a special case of choosing any element of $B^*$, consi …
- 6,237
7
votes
Accepted
Can a positive polynomial on sphere be represented as the sum of squares of spherical harmonics
This Wikipedia page has many references: https://en.wikipedia.org/wiki/Positive_polynomial, including for example
Marshall, Murray Positive polynomials and sums of squares. Mathematical Surveys and …
- 6,237
9
votes
General principles which lead to good questions in many concrete situations
I suggest two "general principles which lead to good questions in many concrete situations": making "abstract" results more explicit, and making explicit results more abstract.
I think these things a …
- 6,237
3
votes
An inner product on the vector space $\mathbb{R}[x_1,\cdots,x_n]_m$
A general expression of $\langle f, g \rangle$ not using integral expressions is quite simple: interpret $f$ as acting on $g$ by differentiation, i.e., replace each $x_i$ in $f$ with $\frac{\partial}{ …
- 6,237
1
vote
About local maxima of multivariable polynomials
The set of critical points (in the domain) of a polynomial is the solution set of a system of polynomial equations viz the vanishing of the first derivatives. So it has finitely many irreducible compo …
- 6,237