Titlebook: Lie Groups, Differential Equations, and Geometry; Advances and Surveys Giovanni Falcone Book 2017 Springer International Publishing AG 2017

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Remarks on Infinite-Dimensional Representations of the Heisenberg Algebra,of the Heisenberg Lie algebra, we sketch the essential features of this interaction, distinguishing in particular the cases of . and . representations. While integrable representations are well understood, nonintegrable representations are quite mysterious objects. We present here a short and didact

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Cohomology Operations Defining Cohomology Algebra of the Loop Space, sequence of operations ..:?..(.). → ..(.),?. = 2,?3,?. which form a minimal ..-algebra (..(.),?{..}). This structure defines on the bar construction ..(.) a correct differential .. so that (..(.),?..) gives cohomology modules of the loop space ..(.). In this paper we construct algebraic operations

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An Optimal Control Problem for a Nonlocal Problem on the Plane,irst order on the plane with nonlocal Bitsadze–Samarski boundary conditions. A?theorem of the existence and uniqueness of a generalized solution in the space . is proved for quasilinear differential equations; necessary conditions of optimality are obtained in terms of the principle of maximum; the

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On the Geometry of the Domain of the Solution of Nonlinear Cauchy Problem,iven functions described the initial conditions are defined on a closed interval. We study also a variant of the inverse problem of the Cauchy problem and prove that the considered inverse problem has a solution under certain regularity condition. We illustrate the Cauchy and the inverse problems in

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