Table of contents

Contents Introduction Chapter I. GG-functions of one variable §1. GG-systems and GG-functions 1.1. Definition of a GG-system 1.2. Reduction to functions of one variable 1.3. Description of the solutions 1.4. The operators L_k 1.5. GG-series 1.6. Relation to the Fox H-functions 1.7. A remark on the definition of a GG-system §2. Integral representations §3. Relation to hypergeometric functions of one variable 3.1. Hypergeometric systems 3.2. Bases in the solution space 3.3. The case of a vector with coordinates 3.4. Relation between the GG-series and the Pochhammer series Chapter II. General GG-functions §4. GG-systems and GG-functions 4.1. The definition of a GG-system 4.2. Another description of the GG-systems 4.3. Special cases 4.4. Differential equations for GG-functions 4.5. Reduced GG-functions §5. Description of the solutions of a GG-system 5.1. Statement of the problem 5.2. The main theorem 5.3. Operators L_k 5.4. The GG-series §6. Integral representations 6.1. Statement of the problem 6.2. The case dim L = N – 1 6.3. The case dim L < N – 1 §7. Connection with general hypergeometric functions 7.1. General hypergeometric functions 7.2. Γ-series associated with bases 7.3. Connection between the GG-series and the Γ-series 7.4. Integral representations 7.5. Main theorem §8. Resonance GG-systems 8.1. Definition of a resonance GG-system 8.2. Description of resonance GG-systems 8.3. Resonance relations 8.4. An example of a resonance system

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Contents Introduction Chapter I. Duality of non-convex extremal problems §1.0. Definitions §1.1. Conjugate functions §1.2. Characterization of convexity in terms of smoothness §1.3. Minimax theorems §1.4. A function conjugate to the maximum of a family of quadratic forms §1.5. Duality of non-convex extremal problems in the case of smoothness of the dual problem Chapter II. Minimax estimation of parameters in linear models of observation with unspecified statistics of the second order §2.1. Formulation of the problem §2.2. Duality theorem §2.3. Minimax estimators and the least squares method §2.4. Linearity of minimax estimators Chapter III. Applications to the theory of ill-posed problems §3.1. Formulation of the problem §3.2. Duality theorem §3.3. The Kuks-Ol'man estimator §3.4. Non-symmetric constraints on the regression parameters

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Contents Introduction §0. Agreements, definitions and preliminaries §1. Surfaces of constant negative curvature §2. Measure rigidity of the horocycle flow §3. Geometric generalizations of Ratner's theorem on measure rigidity of the horocycle flow §4. Quotients and joinings of the horocycle flow §5. Rigidity, quotients and joinings of unipotent flows §6. Dynamics of the horocycle flow §7. Classification of ergodic measures for unipotent flows §8. Uniform distribution of unipotent trajectories §9. Various problems of convergence in the space of measures §10. Structure of orbits, minimal sets, and ergodic measures of homogeneous flows §11. Multiple mixing and measure rigidity of homogeneous flows §12. Ergodic measures and orbit closures for actions of arbitrary subgroups §13. Unipotent flows on homogeneous spaces over local fields §14. Applications to number theory §15. Some open problems

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