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Mathematical physics --- Transformation groups --- Groups of transformations --- Group theory --- Topology --- Transformations (Mathematics) --- Physical mathematics --- Physics --- Mathematics --- Transformation groups. --- Mathematical physics.

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This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

Closed operators. --- Banach spaces. --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Functions of complex variables --- Generalized spaces --- Topology --- Operators, Closed --- Linear operators --- Operateurs lineaires --- Theorie spectrale --- Espaces de banach

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This book consists of a carefully constructed sequence of questions which will enable the reader, through his or her own participation, to generate all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of M bius transformations and stereographic projection, are also included. Quaternions and their relationship to 3dimensional isometrics are covered, and the climax of the book is a study of crystallographic groups, with a complete analysis of these groups in two dimensions.

Geometry --- Group theory --- Transformation groups --- 512.54 --- Groups of transformations --- Topology --- Transformations (Mathematics) --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematics --- Euclid's Elements --- 512.54 Groups. Group theory --- Groups. Group theory --- Geometry. --- Group theory. --- Transformation groups. --- Théorie des groupes --- Transformations, Groupes de --- Géométrie --- Groupes, Théorie des. --- Groupes, Théorie des --- Géometrie --- Géometrie --- Groupes, Théorie des. --- Groupes, Théorie des

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This book introduces the lattice approach to quantum field theory. The spectacular successes of this technique include compelling evidence that exchange of gauge gluons can confine the quarks within subnuclear matter. The lattice framework enables novel schemes for quantitative calculation and has caused considerable cross-disciplinary activity between elementary particle and solid state physicists. The treatment begins with the lattice definition of a path integral and ends on Monte Carlo simulation methods. Other topics include invariant group integration, duality, mean field theory and renormalization group techniques. The reader is assumed to have a basic background in relativistic quantum mechanics and some exposure to gauge theories.

Elementary particles --- 539.1 --- Field theory (Physics) --- Lattice theory --- Particles (Nuclear physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Crystallography, Mathematical --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Symmetry (Physics) --- Classical field theory --- Continuum physics --- Continuum mechanics --- Nuclear physics. Atomic physics. Molecular physics --- Lattice theory. --- Field theory (Physics). --- Particles (Nuclear physics). --- 539.1 Nuclear physics. Atomic physics. Molecular physics --- Gauge fields (Physics) --- Transformations (Mathematics) --- Physics --- Gauge fields (Physics). --- Quarks. --- Quarken.