# Tagged Questions

**0**

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28 views

### Green's function of the Ornstein-Uhlenbeck operator

Consider $\mathbb R^d$ with the Gaussian measure $d\gamma(x) = e^{\frac{1}{4}|x|^2}\,dx$. The Ornstein-Uhlenbeck operator $L$ is given by
$$
Lu = \Delta u- \frac{1}{2}x\cdot \nabla u.
$$
Is there a ...

**2**

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86 views

### “Direct” proof (without hypercontractivity) of equivalence of moments?

Let $(x_i)_{i \in \mathbb{N}}$ be a family of independent $\pm 1$ centered Bernoulli random variables, and let $p, q > 1$. There exists a constant C such that for every (finite) linear combination ...

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49 views

### Hermite coefficients of a positive density

It is well known that a necessary condition for a function in $L_2$ to be a.e. positive is that its fourier transform is positive-definite (in fact, due to Bochner's theorem, this is also a sufficient ...

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748 views

### The Fourier Transform of taking Eigenvalues

The purpose of this question is to ask about the Fourier transform of the map which associate to an $n$ by $n$ matrix its $n$ eigenvalues, or some function of the $n$ eigenvalues. The main motivation ...

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566 views

### Hardy spaces: analysis <---> martingales

Let $H^p$ be the Hardy space of analytic functions on the open unit disk $D$: $f \in H^p$ if $f$ is analytic on $D$ and $\sup_{r < 1} \int_0^{2\pi} |f(re^{i\theta})|^p d\theta < \infty$.
...

**4**

votes

**1**answer

382 views

### When does a matrix define a convolution operator on a hypergroup?

Let $H$ be a discrete hypergroup. Suppose I have a matrix $A=(A_{x,y})$ indexed over $H$ with nonnegative entries which defines a bounded operator on $\ell^2(H)$. When does there exist $f\in\ell^1(H)$ ...