V. Sharafutdinov

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math.AP2025

Range characterization of the ray transform on Sobolev spaces of symmetric tensor fields in two dimensions

Divyansh Agrawal, Venkateswaran P. Krishnan, Vladimir A. Sharafutdinov

The ray transform $I_{m}$ integrates a symmetric $m$ rank tensor field $f$ on $R^{n}$ over lines. In the case of $n \geq 3$ , the range characterization of the operator $I_{m}$ on w…

math.AP2024

Normal operators for momentum ray transforms, I: The inversion formula

Shubham R. Jathar, Manas Kar, Venkateswaran P. Krishnan +1

The momentum ray transform $I_{m}^{k}$ integrates a rank $m$ symmetric tensor field $f$ on $R^{n}$ over lines with the weight $t^{k}$ , $I_m^kf(x,Î¾)=\int_{-\infty}^\infty t^k\langl…

math.AP2024

Normal operators for momentum ray transforms, II: Saint Venant operator

Shubham R. Jathar, Manas Kar, Venkateswaran P. Krishnan +1

The momentum ray transform $I_{m}^{k}$ integrates a rank $m$ symmetric tensor field $f$ on $R^{n}$ over lines with the weight $t^{k}$ , $I_m^kf(x,Î¾)=\int_{-\infty}^\infty t^k\lan…