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Results tagged with fa.functional-analysis
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user 28161
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
5
votes
3
answers
2k
views
Multivariate Hermite Polynomials
Let $h_0, h_1, \dots$ be the classical univariate Hermite polynomials, renormalized to have constant norm. Is
$$x\mapsto\prod_{j=1}^n h_{l_j}(x_j), \quad l_j\in \mathbb N$$
a complete orthogonal syste …
- 293
4
votes
1
answer
296
views
Rank of a sequence of covariance matrices
Let $X_i$ ($i=1, \dots$) be an orthonormal basis for $L^2(\Omega, \mathbb P)$. In particular, it holds that
$$\mathbb E[X_iX_j] = \delta_{ij}.$$
Now take $Z\in L^2(\Omega, \mathbb P)$ and define $\ti …
- 293