V. Sharafutdinov

activity

20242026

most citedNormal operators for momentum ray transforms, I: The inversion formula

4 citations · 5 across the 6 of their papers we have counts for

collaborators

7 papers

math.DG2026

Numerical solution of the two-dimensional Calderón problem based on the Hilbert transform of a planar domain

Sagar Gohri, Vladimir Sharafutdinov

Let $(M, g)$ be a $C^{\infty}$ smooth compact connected Riemannian manifold with boundary $\partial M$ . Consider the Dirichlet problem: $Δ_{g} u = 0, u ∣_{\partial M} = f$ for $f\in C^{\in…

math.DG2026

Numerical solution of the two-dimensional Calderon problem for domains close to a disk

Vladimir A. Sharafutdinov, Konstantin V. Storozhuk

For a compact Riemannian surface $(M, g)$ with non-empty boundary $Γ$ , the Dirichlet-to-Neumann operator (DtN-map) $Λ_{g} : C^{\infty} (Γ) \to C^{\infty} (Γ)$ is defined by $Λ_gf=\left.\frac{\…

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.DG2025

Two-dimensional Calderon problem and flat metrics

Vladimir A. Sharafutdinov

For a compact Riemannian manifold $(M, g)$ with boundary $\partial M$ , the Diri\-chl\-et-to-Neumann operator $Λ_{g} : C^{\infty} (\partial M) ⟶ C^{\infty} (\partial M)$ is define…

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,ξ)=\int_{-\infty}^\infty t^k\lang…

math.AP2024★ 1 cited

Ray transform on Sobolev spaces of symmetric tensor fields, II: Range characterization

Venky P. Krishnan, Vladimir A. Sharafutdinov

The ray transform $I$ integrates symmetric $m$ -tensor field in $R^{n}$ over lines. This transform in Sobolev spaces was studied in our earlier work where higher order Reshet…

math.AP2024★ 4 cited

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,ξ)=\int_{-\infty}^\infty t^k\langle…