All Questions

Disclaimer: Let me apologize in advance for asking this slightly vague question Let $M$ be a manifold and let $P$ be a partial differential operator acting on $C^{\infty}(M)$. Associated to $P$ there'...

In the litterature, in particular in the papers on dynamical investigation of polynomial vector fields on the plane, are there some research devoting to study the Green's function for the PDE which is ...

Let $A$ be the algebra of all smooth functions $f: \mathbb{R}^2 \to \mathbb{R}$ such that $f$ is flat at the origin and is real analytic on $\mathbb{R}^2 \setminus \{0\}$. Let $B $ be ...

We fix a Hilbert space isomorphism $\phi:H^{1}\to H^{2}$. Here by $H^{s},\;s=1,2,\;$ we mean the sobolev space on $\mathbb{R}^{2}$ or $S^{2}$. We consider the following polynomial vector field on ...

A polynomial vector field of degree $n$ on $S^{2}$ is the Poincare compactification of a $n$ degree polynomial vector field on $\mathbb{R}^{2}$.It is a real analytic vector field on $S^{2}$ which ...

Added, June 19, 2019: The main motivation of this post is to associate an index to differential operator associated to a dynamical system such that the index has an interesting ...