Table of contents

Contents Introduction § 1. Parabolic submanifolds 1.1. Point structure of the space of second fundamental forms of a k-parabolic surface 1.2. Normal bundle of a manifold 1.3. Local structure of the k-parabolic submanifolds in a Riemannian space 1.4. Complete parabolic submanifolds of a Riemannian space 1.5. Pontryagin characteristic classes of parabolic submanifolds in a spherical space § 2. k-saddle and k-convex submanifolds 2.1. Topological structure of saddle submanifolds 2.2. Intersection of saddle submanifolds in a Riemannian space 2.3. k-asymptotic and k-convex submanifolds § 3. Submanifolds of non-positive extrinsic curvature 3.1. Extrinsic curvature 3.2. Foliations on Riemannian manifolds 3.3. Affinely stable immersions of Riemannian metrics

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Contents § 1. Introduction § 2. Notation and definitions § 3. Prototypes of wavelets in Calderón's and Luzin's papers § 4. The Gabor transform § 5. The windowed Fourier transform § 6. The integral wavelet transform § 7. Dyadic wavelets and inversion formulae § 8. Frames § 9. Wavelet series § 10. The Haar system on the real line § 11. Multiresolution analysis in § 12. The Whittaker-Shannon-Kotel'nikov system § 13. Uncertainty constants § 14. Meyer wavelets § 15. Lemarié-Battle and Strömberg wavelets § 16. Orthogonal compactly supported wavelets § 17. Fast algorithms § 18. Semi-orthogonal compactly supported spline wavelets § 19. Regular multiresolution analyses in § 20. Bernstein inequalities § 21. Regular multiresolution analyses and polynomials § 22. Multiresolution analyses in Sobolev spaces § 23. The operators § 24. Besov spaces § 25. The projections and pseudo-differential operators § 26. A wavelet characterization of the Hölder spaces , the Sobolev spaces , and the Besov spaces  § 27. A wavelet characterization of the spaces and BMO § 28. A wavelet characterization of the spaces and § 29. Periodic wavelets

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Contents Introduction § 1. Controlled random sequences: main definitions and traditional approaches § 1.1. Description of the mathematical model § 1.2. Models with integral functionals § 1.3. Homogeneous Markov decision processes with average cost criteria § 2. Application of methods of convex analysis § 2.1. Properties of the space  § 2.2. Existence of optimal policies § 2.3. Sufficiency of selectors § 2.4. Preliminary results. The notion of an occupation measure § 2.5. Markov decision processes with total cost criteria and occupation measures § 2.6. Discounted costs and the corresponding occupation measures § 2.7. Average costs and ergodic occupation measures § 3. Problems with functional constraints § 3.1. General results § 3.2. Preliminary conclusions § 3.3. Markov decision processes with total cost criteria § 3.4. Homogeneous Markov decision processes with discounting § 3.5. Homogeneous Markov decision processes with average cost criteria § 3.6. Other constrained problems, related topics, and future prospects Conclusion Appendix. Elements of convex analysis and measure theory

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Contents I. Introduction II. General considerations § 1. Quantum communication channel § 2. Entropy bound and channel capacity § 3. Formulation of the quantum coding theorem. Weak conversion III. Proof of the direct statement of the coding theorem § 1. Channels with pure signal states § 2. Reliability function § 3. Quantum binary channel § 4. Case of arbitrary states with bounded entropy IV. c-q channels with input constraints § 1. Coding theorem § 2. Gauss channel with one degree of freedom § 3. Classical signal on quantum background noise

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