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Geometry, Differential. --- Noncommutative algebras. --- Mathematical physics. --- Physical mathematics --- Physics --- Algebras, Noncommutative --- Non-commutative algebras --- Algebra --- Differential geometry --- Mathematics --- Mathematical analysis
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"The algebraic theory of automata was created by Schutzenberger and Chomsky over 50 years ago and there has since been a great deal of development. Classical work on the theory to noncommutative power series has been augmented more recently to areas such as representation theory, combinatorial mathematics and theoretical computer science. This book presents to an audience of graduate students and researchers a modern account of the subject and its applications. The algebraic approach allows the theory to be developed in a general form of wide applicability. For example, number-theoretic results can now be more fully explored, in addition to applications in automata theory, codes and non-commutative algebra. Much material, for example, Schutzenberger's theorem on polynomially bounded rational series, appears here for the first time in book form. This is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap"--
Machine theory --- Noncommutative algebras --- Automates mathématiques, Théorie des --- Algèbres non commutatives --- Automates mathématiques, Théorie des --- Algèbres non commutatives --- Machine theory. --- Noncommutative algebras. --- Automates. --- Algèbres non commutatives. --- Algebras, Noncommutative --- Non-commutative algebras --- Algebra --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics --- Algèbres non commutatives.
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Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.
Noncommutative differential geometry. --- Mathematics. --- Fourier analysis. --- Functional analysis. --- Integral equations. --- Operator theory. --- Numerical analysis. --- Equations, Integral --- Functional calculus --- Analysis, Fourier --- Math --- Differential geometry, Noncommutative --- Geometry, Noncommutative differential --- Non-commutative differential geometry --- Functional Analysis. --- Numerical Analysis. --- Integral Equations. --- Operator Theory. --- Fourier Analysis. --- Mathematical analysis --- Functional analysis --- Functional equations --- Calculus of variations --- Integral equations --- Science --- Infinite-dimensional manifolds --- Operator algebras --- Gelfand-Naimark theorem. --- Noncommutative algebras.
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