Stability estimates with a priori bound for the inverse local Radon transform

Jan Boman; Joel Andersson

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Stability estimates with a priori bound for the inverse local Radon transform

Joel Andersson, Jan Boman

Analysis of PDEs · Submitted 15 May 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For weight functions satisfying a certain differential equation we give weak estimates of $f$ in terms of $R_m[f]$ for functions $f$ that satisfies an a priori bound.

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We consider the inverse problem for the $2$-dimensional weighted local Radon transform $R_m[f]$, where $f$ is supported in $y\geq x^2$ and $R_m[f](\xi,\eta)=\int f(x, \xi x + \eta) m(\xi, \eta, x)\,\text{d} x$ is defined near $(\xi,\eta)=(0,0)$. For weight functions satisfying a certain differential equation we give weak estimates of $f$ in terms of $R_m[f]$ for functions $f$ that satisfies an a priori bound.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider the inverse problem for the $2$-dimensional weighted local Radon transform $R_m[f]$, where $f$ is supported in $y\geq x^2$ and $R_m[f](\xi,\eta)=\int f(x, \xi x + \eta) m(\xi, \eta, x)\,\text{d} x$ is defined near $(\xi,\eta)=(0,0)$.	background 0.78	0.41	0.05	asserted 0.92
s1	For weight functions satisfying a certain differential equation we give weak estimates of $f$ in terms of $R_m[f]$ for functions $f$ that satisfies an a priori bound.	result 0.71	0.92	0.83	asserted 1.00

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Original abstract

We consider the inverse problem for the $2$-dimensional weighted local Radon transform $R_m[f]$, where $f$ is supported in $y\geq x^2$ and $R_m[f](\xi,\eta)=\int f(x, \xi x + \eta) m(\xi, \eta, x)\,\text{d} x$ is defined near $(\xi,\eta)=(0,0)$. For weight functions satisfying a certain differential equation we give weak estimates of $f$ in terms of $R_m[f]$ for functions $f$ that satisfies an a priori bound.

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