Integral geometry of tensor fields

著者

• Sharafutdinov, V. A. (Vladimir Alʹtafovich)

書誌事項

Integral geometry of tensor fields

V.A. Sharafutdinov

（Inverse and ill-posed problems series）

VSP, 1994

注記

Bibliography: p. 259-268

Includes index

内容説明・目次

内容説明

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

目次

INTRODUCTION The problem of determining a metric by its hodograph and a linearization of the problem The kinetic equation on a Riemannian manifold Some remarks THE RAY TRANSFORM OF SYMMETRIC TENSOR FIELDS ON EUCLIDEAN SPACE The ray transform and its relationship to the Fourier transform Description of the kernel of the ray transform in the smooth case Equivalence of the first two statements of Theorem 2.2.1 in the case n = 2 Proof of Theorem 2.2.2 The ray transform of a field-distribution Decomposition of a tensor field into potential and solenoidal parts A theorem on the tangent component A theorem on conjugate tensor fields on the sphere Primality of the ideal ([x]2, (x,y)) Description of the image of the ray transform Integral moments of the function If Inversion formulas for the ray transform Proof of Theorem 2.12.1 Inversion of the ray transform on the space of field-distributions The Plancherel formula for the ray transform Application of the ray transform to an inverse problem of photoelasticity Further results SOME QUESTIONS OF TENSOR ANALYSIS Tensor fields Covariant differentiation Symmetric tensor fields Semibasic tensor fields The horizontal covariant derivative Formulas of Gauss--Ostrogradskii type for vertical and horizontal derivatives THE RAY TRANSFORM ON A RIEMANNIAN MANIFOLD Compact dissipative Riemannian manifolds The ray transform on a CDRM The problem of inverting the ray transform Pestov's differential identity Poincare's inequality for semibasic tensor fields Reduction of Theorem 4.3.3 to an inverse problem for the kinetic equation Proof of Theorem 4.3.3 Consequences for the nonlinear problem of determining a metric from its hodograph Bibliographical remarks THE TRANSVERSE RAY TRANSFORM Electromagnetic waves in quasi-isotropic media The transverse ray transform on a CDRM Reduction of Theorem 5.2.2 to an inverse problem for the kinetic equation Estimation of the summand related to the right-hand side of the kinetic equation Estimation of the boundary integral and summands depending on curvature Proof of Theorem 5.2.2 Decomposition of the operators A0 and A1 Proof of Lemma 5.6.1 Final remarks THE TRUNCATED TRANSVERSE RAY TRANSFORM The polarization ellipse The truncated transverse ray transform Proof of Theorem 6.2.2 Decomposition of the operator Q, Proof of Lemma 6.3.1 Inversion of the truncated transverse ray transform on Euclidean space THE MIXED RAY TRANSFORM Elastic waves in quasi-isotropic media The mixed ray transform Proof of Theorem 7.2.2 The algebraic part of the proof THE EXPONENTIAL RAY TRANSFORM Formulation of the main definitions and results The modified horizontal derivative Proof of Theorem 8.1.1 The volume of a simple compact Riemannian manifold Determining a metric in a prescribed conformal class Bibliographical remarks Bibliography Index

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詳細情報

• NII書誌ID(NCID): BA24205952
• ISBN:
  • 9067641650
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Utrecht
• ページ数/冊数: 271 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA2420606X