The contraction-mapping tag has no usage guidance.

**4**

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192 views

### On the possibility of extending the Sz.-Nagy dilation theorem for multiple contraction operators on Hilbert spaces

I am presently doing research concerned with operator algebras and operator theory and I thought to write here in the hopes of seeking expert advice on an idea I had here. The classic Sz.-Nagy ...

**4**

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108 views

### On contractive properties of a nonlinear matrix algorithm

I’m stuck in a problem that concerns a nonlinear iterative matrix algorithm.
Although the problem is quite complicated to explain I’ll try to describe it in a simple way, neglecting unnecessary ...

**3**

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**1**answer

152 views

### Convergence of trajectories and asymptotic stability

Say that an autonomous system $\dot{u} = f(u)$ in $\mathbb{R}^{m}$ has the property that for any two solutions $x(t), y(t)$ corresponding to initial conditions $x(0)$ and $y(0)$ the trajectories are ...

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54 views

### Unfolding subspace algebraic space

Let $ Y \subset X$ be a closed subspace of an algebraic space of finite type over $\mathbb{C}$. Let $p : Y' \rightarrow Y$ be a proper map of algebraic spaces. Artin proved that there exists a ...

**2**

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**1**answer

175 views

### Does a particular iteration produce a weak solution to a non linear pde?

Consider the following non linear pde in the unknown $v(x,y)$:
$$ \frac{\partial v(x,y)}{\partial x} +
\Big(\frac{\partial v(x,y)}{\partial x} \Big)^2 = e^{2 ty}-1 $$
where $t$ is some fixed small ...

**5**

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**0**answers

190 views

### Is there an appropriate weighted Sobolev space to include exponential map and projection map?

Observe that given a non negative function
$\omega: \mathbb{R^2} \rightarrow [0, \infty)$, we can define the weighted
$L^{p}(\mathbb{R}^2, \omega) $ spaces. They are measurable functions
$f: \...