# Questions tagged [pseudo-differential-operators]

This tag is for questions regarding to pseudo-differential operators, which are generalizations of differential operators and Fourier multipliers. It satisfies estimates for the derivatives analogous to the estimates for derivatives of polynomials, which are symbols of differential operators.

120 questions
Filter by
Sorted by
Tagged with
1 vote
23 views

### Limiting behavior of integral representation of $(\sqrt{\alpha^2-\partial_x^2}-\alpha)f(x)$

While studying pseudo-differential operators of type $\left(\sqrt{\alpha^{2} - \partial_{x}^{2}}-\alpha\right)\operatorname{f}\left(x\right)$, I came across the following integral representation of ...
• 827
21 views

### About evolution problem with variable coefficients.

I'm studying differential operators. For example, in the evolution equation \begin{align} u_t&=(1-\partial_x^2)u\\ u(0)&=u_0 \end{align} Question 1. Does this problem have any name in the ...
• 3,630
18 views

### Spectral theory for this kind of operators

Let $a(x,\xi)$ be the symbol for a differential operator $$|\partial^{\alpha}_{x}\, \partial^{\beta}_{\xi} a(x,\xi)| \leq C (1+|x|+|\xi|)^{m-|\alpha|-|\beta|}$$ $|x|+|\xi|\geq c$. Is there a spectral ...
• 127
1 vote
50 views

1 vote
95 views

• 3,630