دانلود کتاب Operator Theory and Ill-Posed Problems

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BASIC CONCEPTS\nChapter 1. Set theory\n1.1 Sets\n1.2 Correspondences\n1.3 Relations\n1.4 Induction\n1.5. Natural numbers\nChapter 2. Algebra\n2.1 Abstract algebra\n2.2 Linear algebra\n2.3 Multilinear algebra\nChapter 3. Calculus\n3.1. Limit\n3.2. Differential\n3.3 Integral\n3.4 Analysis on manifolds\nOPERATORS\nChapter 4. Linear operators\n4.1 Hubert spaces\n4.2 Fourier series\n4.3. Function spaces\n4.4 Fourier transform\n4.5 Bounded linear operators\n4.6 Compact linear operators\n4.7 Self-adjoint operators\n4.8 Spectra of operators\n4.9. Spectral theorem\n4.10. Operator exponential\nChapter 5. Nonlinear operators\n5.1 Fixed points\n5.2 Saddle points\n5.3 Monotonie operators\n5.4 Nonlinear contractions\n5.5 Degree theory\nILL-POSED PROBLEMS\nChapter 6. Classic problems\n6.1 Mathematical description of the laws of physics\n6.2 Equations of the first order\n6.3 Classification of differential equations of the second order\n6.4 Elliptic equations\n6.5 Hyperbolic and parabolic equations\n6.6 The notion of well-posedness\nChapter 7. Ill-posed problems\n7.1 Ill-posed Cauchy problems\n7.2 Analytic continuation and interior problems\n7.3. Weakly and strongly ill-posed problems. Problems of differentiation\n7.4. 7.4 Reducing ill-posed problems to integral equations\nChapter 8. Physical problems leading to ill-posed problems\n8.1 Interpretation of measurement data from physical devices\n8.2 Interpretation of gravimetric data\n8.3 Problems for the diffusion equation\n8.4 Determining physical fields from the measurements data\n8.5 Tomography\nChapter 9. Operator and integral equations\n9.1 Definitions of well-posedness\n9.2 Regularization\n9.3 Linear operator equations\n9.4 Integral equations with weak singularities\n9.5 Scalar Volterra equations\n9.6Volterra operator equations\nChapter 10. Evolution equations\n10.1 Cauchy problem and semigroups of operators\n10.2 Equations in a Hilbert space\n10.3 Equations with variable operator\n10.4 Equations of the second order\n10.5 Well-posed and ill-posed Cauchy problems\n10.6 Equations with integro-differential operators\nChapter 11. Problems of integral geometry\n11.1 Statement of problems of integral geometry\n11.2 The Radon problem\n11.3 Reconstructing a function from spherical means\n11.4 Planar problem of the general form\n11.5 Spatial problems of the general form\n11.6 Problems of the Volterra type for manifolds invariant with respect to the translation group\n11.7 Planar problems of integral geometry with a perturbation\nChapter 12. Inverse problems\n12.1Statement of inverse problems\n12.2 Inverse dynamic problem. A linearization method\n12.3. A general method for studying inverse problems for hyperbolic equations\n12.4 The connection between inverse problems for hyperbolic, elliptic, and parabolic equations\n12.5 Problems of determining a Riemannian metric\nChapter 13. Several areas of the theory of ill-posed problems, inverse problems, and applications\nBibliography\nIndex