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Fluid mechanics --- Turbulence --- Turbulence. --- 532.517.4 --- #KVIV:BB --- Turbulent flow --- 532.517.4 Turbulent flow --- Flow, Turbulent --- Fluid dynamics

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Approximation theory --- 517.518.8 --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Approximation of functions by polynomials and their generalizations --- 517.518.8 Approximation of functions by polynomials and their generalizations

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The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.

Hyperfunctions --- Microlocal analysis --- Hyperfunctions. --- Microlocal analysis. --- Hyperfonctions --- Hyperfuncties --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Analysis. --- Partial Differential Equations. --- Partial differential equations --- 517.1 Mathematical analysis --- Mathematical analysis

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Quantum groups --- 517.986 --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Quantum theory --- Théorie des groupes --- Théorie quantique

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Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.

Manifolds (Mathematics). --- Mathematical analysis. --- Mathematical physics. --- Manifolds (Mathematics) --- Mathematical analysis --- Mathematical physics --- 514.84 --- Physical mathematics --- Physics --- 514.84 Geometric methods in quantum mechanics and in the theory of elementary particles --- Geometric methods in quantum mechanics and in the theory of elementary particles --- 517.1 Mathematical analysis --- Geometry, Differential --- Topology --- Mathematics --- 514.8 --- 514.8 Geometric study of objects of mechanics and physics --- Geometric study of objects of mechanics and physics --- 517.1. --- Analyse mathématique --- Variétés (Mathématiques) --- Physique mathématique --- ELSEVIER-B EPUB-LIV-FT --- 517.1