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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

Ordered algebraic structures --- Operator theory --- Analyse fonctionnelle --- Functional analysis --- Linear operators. --- Banach spaces. --- Operator ideals. --- Linear operators --- Ideals (Algebra) --- Banach spaces --- Operator ideals --- 517.983 --- 517.983 Linear operators. Linear operator equations --- Linear operators. Linear operator equations --- Linear maps --- Maps, Linear --- Operators, Linear --- Functions of complex variables --- Generalized spaces --- Topology --- Functional analysis. --- Espaces d'operateurs lineaires continus --- Espaces de banach --- Ideaux normes --- Operateurs lineaires

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Holomorphic maps and invariant distances

Analytical spaces --- Banach spaces. --- Holomorphic mappings. --- Domains of holomorphy. --- Distance geometry. --- Abstract metrics --- Metric topology --- Metric spaces --- Topology --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Mappings, Holomorphic --- Mappings (Mathematics) --- Functions of complex variables --- Generalized spaces --- Banach spaces --- Distance geometry --- Domains of holomorphy --- Holomorphic mappings --- 517.55 --- 517.982 --- 517.982 Linear spaces with topology and order or other structures --- Linear spaces with topology and order or other structures --- 517.55 Functions of several complex variables. Approximation. Integral representations. Holomorphic functions. Entire functions --- Functions of several complex variables. Approximation. Integral representations. Holomorphic functions. Entire functions

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Differential equations, Partial --- Hilbert space --- Equations aux dérivées partielles --- Espace de Hilbert --- 517.95 --- Banach spaces --- Hyperspace --- Inner product spaces --- Partial differential equations --- Differential equations, Partial. --- Hilbert space. --- Solution --- Hilbert space methods --- Hilbert space methods. --- 517.95 Partial differential equations --- Equations aux dérivées partielles