fa.functional analysis – Continuity of Radon transform w.r.t the angle Answer

plane geometry - Does the intersection of two moving curves sweep out a continuous line?

Hello dear visitor to our network We will offer you a solution to this question fa.functional analysis – Continuity of Radon transform w.r.t the angle ,and the answer will be typical through documented information sources, We welcome you and offer you new questions and answers, Many visitor are wondering about the answer to this question.

fa.functional analysis – Continuity of Radon transform w.r.t the angle

let $f \in L^1(\mathbb R^n)$ (or in case it helps, actually a probability density on $\mathbb R^n$). fix $b \in \mathbb R$ and define the Radon transform $R[f]:S_{n-1} \times \mathbb R \to \mathbb R$ of $f$ by

$$R[f](w,b) := \int_{\mathbb R^n}\delta(x^\top w – b)f(x)\,dx, $$

where $S_{n-1}$ is the unit-sphere in $\mathbb R^n$.

question. Under what minimal additional conditions on $f$ is mapping $w \mapsto R[f](w,b)$ continuous continuous on $S_{n-1}$for each $b \in \mathbb R$ ?

we will offer you the solution to fa.functional analysis – Continuity of Radon transform w.r.t the angle question via our network which brings all the answers from multiple reliable sources.