A. L. Bukhgeim
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
A. L. Bukhgeim has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
- Masahiro Yamamoto
Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
4 shared publications - Eduard Vitalievich Arbuzov
Kutateladze Institute of Thermophysics of the Siberian Branch of the Russian Academy of Sciences
2 shared publications - Sergey Gavrilovich Kazantsev
Sobolev Institute of Mathematics
2 shared publications - E. V. Tantserev
Sobolev Institute of Mathematics
1 shared publication G. Uhlmann
University of Washington, Seattle, USA.
1 shared publication- G. V. Dyatlov
Sobolev Institute of Mathematics, Novosibirsk, Russia.
1 shared publication
Latest Publications
- 26 November 2007
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 15 (6) , 587-598
Unique continuation for hyperbolic equations with memory
We prove the unique continuation property for the hyperbolic integro-differential equation
- 26 November 2007
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 15 (6) , 587-598
Unique continuation for hyperbolic equations with memory
We prove the unique continuation property for the hyperbolic integro-differential equation
- 1 May 2006
- Published by Springer Nature in Siberian Mathematical Journal
- Vol. 47 (3) , 425-432
The Carleman formula for the Helmholtz equation on the plane
- 1 May 2006
- Published by Springer Nature in Siberian Mathematical Journal
- Vol. 47 (3) , 425-432
The Carleman formula for the Helmholtz equation on the plane
- 1 July 2004
- Published by Springer Nature in Siberian Mathematical Journal
- Vol. 45 (4) , 618-627
Uniqueness in One Inverse Problem for the Elasticity System
- 1 July 2004
- Published by Springer Nature in Siberian Mathematical Journal
- Vol. 45 (4) , 618-627
Uniqueness in One Inverse Problem for the Elasticity System
- 1 June 2004
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 12 (3) , 245-278
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc as the operator, acting from the object space L 2 (; S m ) to the data space L 2 ([0, 2π) × [0, 2π)). The orthogonal polynomial basis of solenoidal tensor fields on the disc was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator was obtained. The inversion formula for the fan-beam tensor transform follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.
- 1 June 2004
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 12 (3) , 245-278
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc as the operator, acting from the object space L 2 (; S m ) to the data space L 2 ([0, 2π) × [0, 2π)). The orthogonal polynomial basis of solenoidal tensor fields on the disc was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator was obtained. The inversion formula for the fan-beam tensor transform follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.
- Open Access
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform ${\cal D}_m $ of symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc $\mathbb D$ as the operator, acting from the object space ${\mathbf L}_{2}(\mathbb D; {\bf S}_m)$ to the data space $L_2([0,2\pi)\times[0,2\pi)).$ The orthogonal polynomial basis ${\bf s}^{(\pm m)}_{n,k}$ of solenoidal tensor fields on the disc $\mathbb D$ was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator ${\cal D}_m $ was obtained. The inversion formula for the fan-beam tensor transform ${\cal D}_m $ follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.Open AccessSingular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform ${\cal D}_m $ of symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc $\mathbb D$ as the operator, acting from the object space ${\mathbf L}_{2}(\mathbb D; {\bf S}_m)$ to the data space $L_2([0,2\pi)\times[0,2\pi)).$ The orthogonal polynomial basis ${\bf s}^{(\pm m)}_{n,k}$ of solenoidal tensor fields on the disc $\mathbb D$ was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator ${\cal D}_m $ was obtained. The inversion formula for the fan-beam tensor transform ${\cal D}_m $ follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented. - 1 August 2001
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 9 (4) , 319-326
Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
- The Cauchy problems for operator analogues of the Laplace and Poisson equations with data known on a part of the domain boundary are considered. For solutions of these problems formulas of Carleman type are derived. The formulas obtained can be used in investigation of two-dimensional tomography problems with incomplete data.
- 1 August 2001
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 9 (4) , 319-326
Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
- The Cauchy problems for operator analogues of the Laplace and Poisson equations with data known on a part of the domain boundary are considered. For solutions of these problems formulas of Carleman type are derived. The formulas obtained can be used in investigation of two-dimensional tomography problems with incomplete data.
- 1 January 2001
- Published by Springer Nature
- p. 27-46
Uniqueness in Determining Damping Coefficients in Hyperbolic Equations
- 1 January 2001
- Published by Springer Nature
- p. 27-46
Uniqueness in Determining Damping Coefficients in Hyperbolic Equations
- 1 February 2000
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 242 (1) , 57-74
Conditional Stability in an Inverse Problem of Determining a Non-smooth Boundary
- 1 February 2000
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 242 (1) , 57-74
Conditional Stability in an Inverse Problem of Determining a Non-smooth Boundary
- 1 August 1999
- Published by IOP Publishing in Inverse Problems
- Vol. 15 (4) , 1021-1032
Stability for an inverse boundary problem of determining a part of a boundary
- 1 August 1999
- Published by IOP Publishing in Inverse Problems
- Vol. 15 (4) , 1021-1032
Stability for an inverse boundary problem of determining a part of a boundary
- 1 January 1998
- Published by Elsevier
- p. 327-336
Uniqueness and stability for an inverse problem of determining a part of boundary
- 1 January 1998
- Published by Elsevier
- p. 327-336
Uniqueness and stability for an inverse problem of determining a part of boundary