Introduction to the theory of inverse problems

著者

• Bukhgeĭm, A. L. (Aleksandr Lʹvovich)

書誌事項

Introduction to the theory of inverse problems

A.L. Bukhgeim

（Inverse and ill-posed problems series）

VSP, 2000

注記

Bibliography : p. [225]-232

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

• Chapter 1 Inverse problems for difference operators: inverse problem of spectral analysis for Jacobi matrices
• inverse problem for a difference equation with constant coefficients
• the problems of determining a difference operator in non-stationary statement
• remarks and references. Chapter 2 A priori estimates and the uniqueness of integro-differential equations with operator coefficients: estimates of the Carleman type and their connection with the uniqueness of solutions of inverse problems
• estimates for the Schrodinger equation with operator coefficients
• remarks and references. Chapter 3 Inverse problems for differential equations: one-dimensional inverse problem for the wave equation in linearized statement
• the method of transformation operators
• uniqueness in multidimensional inverse problems in nonstationary and spectral statements
• remarks and references. Chapter 4 Volterra operator equations and their applications: Volterra operator equations in scales of Banach spaces
• non-hyperbolic Cauchy problem for the wave equation
• the problem of integral geometry in a strip
• the inverse problem of variational calculus
• remarks and references. Chapter 5 Foundations of the theory of conditionally well-posed problems: conditional well-posedness lh
• well-posedness of difference schemes
• variational methods of solution of lh-stable difference schemes
• remarks and references. Chapter 6 Theory of stability of difference schemes: statement of the problem and the necessary conditions of finite stability
• basic estimates
• sufficient stability conditions
• estimates of l-stability up to the boundary
• convergence theorems
• finite stability of two-layer schemes of the canonical form
• conditions of stability in terms of the transition operator
• remarks and references.

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詳細情報

• NII書誌ID(NCID): BA46093397
• ISBN:
  • 906764319X
• 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: iv, 232 p.
• 大きさ: 26 cm
• 親書誌ID:
  • BA2420606X