# Tagged Questions

**2**

votes

**1**answer

256 views

### Leibniz rule for Pseudo-differential operators of negative order

Does anyone know of some good references for a fractional Leibniz rule for pseudo-differential operators of negative order? As a specific example, I would like to compute $\partial_{x}^{-1}(uv)$, ...

**1**

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**1**answer

81 views

### Choosing boundary conditions for $(\frac{-d^2}{dx^2})^m$ on $H^m((0,1))$?

Consider the differential operator $D:$
$$
Du:=\frac{-d^2}{dx^2}u
$$
on the function space $$C=\{ u\in C^2([0,1]):u(0)=u(1)=0\}.$$
It's not hard to find the eigenvalues and ...

**4**

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**0**answers

323 views

### Monodromy of differential equations

Let $D$ an ordinary differential equation (let's assume $D$ only has regular singularities). Suppose $D$ = $D_0$$\partial$, where $\partial$ is $q\frac{d}{dq}$ My question is: Does there exist any ...

**3**

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**5**answers

444 views

### Analytic hypoellipticity of linear ordinary differential operators

Let $P = a_n(x) D_x^n + a_{n-1}(x) D_x^{n-1} + \ldots + a_0(x)$ be a linear ordinary differential operator with polynomial (or real analytic) coefficients $a_j(x)$. Suppose that $a_n(x)$ doesn't ...