All Questions

I consider the following scenario. Let $I$ be a compact interval in space and $f$ a nice function in the space $C^{\infty}(I)$. In the following we consider a self-adjoint realization of our operators ...

In a previous question on mathoverflow, I asked about the following: Let $\Delta$ be the Laplacian on some compact interval $I$ of the real line with let's say Dirichlet boundary conditions. The ...

Let $x,y$ be positive real numbers then $$|\sqrt{x}-\sqrt{y}|=\dfrac{|x-y|}{\sqrt{x}+\sqrt{y}}=\sqrt{|x-y|}\cdot \dfrac{\sqrt{|x-y|}}{\sqrt{x}+\sqrt{y}}\leq 1\cdot |x-y|^{\frac{1}{2}}$$ we obtain $1/...

Consider the Schroedinger operator $$H = -\Delta + \frac{c}{\vert x \vert^2}$$ in two dimensions with $c >0$ This operator has a self-adjoint realization, since it is a positive symmetric operator ...

Let $f$ be an arbitrary function in $L^2(0,\infty)$ and consider the function $$(g_f)(y) = \frac{1}{y-x_0} \int_{0}^{\infty} f(x) \left(\frac{xy}{(x^2+y^2+1)}\right)^2 \ dx$$ where $x_0$ is an ...

I was wondering if there is an analogue to the classical Riesz Thorin theorem for Schatten classes. I suppose the answer is yes, since Schatten classes are so similar to $\ell^p$ spaces for which the ...