All Questions

I want to apply the theory of $D$-modules to solve operator equations of several variables in the Bargmann space $$\mathcal H :=\bigg\{\psi \in \mathcal O^\text{an}_{\mathbb{C}^n}\,\,\bigg|\,\,\,\...

Let $q(x)$ be a probability density function over $[0,1]$. Let $\lambda > 0$ and $f: [0,1] \to \mathbb{R}$ be any solution to the following ODE: $$ \lambda f''(x) + q(x) f(x) = 0, \text{for all }x \...

Choose a Schwartz function on $\mathbb C$ of the form $f(z)=f(r e^{i\theta})= f_0(r) e^{in\theta}$. Then $$(*) \quad f(e^{i\alpha} z)= e^{in\alpha} f(z), \quad \forall z\in \mathbb C.$$ Now, let $f$ ...

I have an $ L^2(\mathbb{R}) $ operator that looks like $$ \Omega = \int \partial\phi(a, b)\ \ |b, a\rangle \langle b, a |, $$ where $ \langle x | a, b \rangle = f_a(x - b) e^{x^2/2} $ and $ f_a \in L^...

I'm interested in the existence and/or uniqueness to the following problem. Let $V$ and $H$ be Hilbert spaces and $V \subset H \subset V^*$ form a Gelfand triple. There is a linear operator $L:{D}(L) ...