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Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.
Logic, Symbolic and mathematical --- Algebra, Boolean --- Quasi-metric spaces --- Petri nets --- Set theory --- Spaces, Quasi-metric --- Metric spaces --- Boolean algebra --- Boole's algebra --- Algebraic logic --- Computability theory. --- descriptive set theory. --- non-classical logic.
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The dramatic changes that came about in analysis during the twentieth century are truly amazing. In the thirties, complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calderón-Zygmund school, the action today is taking place in spaces of homogeneous type. No group structure is available and the Fourier transform is missing, but a version of harmonic analysis is still available. Indeed the geometry is conducting the analysis. The authors succeed in generalizing the construction of wavelet bases to spaces of homogeneous type. However wavelet bases are replaced by frames, which in many applications serve the same purpose.
Harmonic analysis --- Spaces of homogeneous type --- Operations Research --- Mathematical Theory --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Harmonic analysis. --- Spaces of homogeneous type. --- Homogeneous type spaces --- Spaces, Homogeneous type --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Approximation theory. --- Fourier analysis. --- Functional analysis. --- Functions of complex variables. --- Functions of a Complex Variable. --- Analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Approximations and Expansions. --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- 517.1 Mathematical analysis --- Math --- Science --- Quasi-metric spaces --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic
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The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis include: * treatment of metrization from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields; * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties.
Functional analysis. --- Nonsymmetric matrices. --- Probabilities. --- Quasi-metric spaces. --- Groupoids --- Harmonic analysis --- Functional analysis --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Operations Research --- Groupoids. --- Harmonic analysis. --- Functional calculus --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Algebraic geometry. --- Mathematical analysis. --- Analysis (Mathematics). --- Measure theory. --- Topology. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Analysis. --- Measure and Integration. --- Algebraic Geometry. --- Calculus of variations --- Functional equations --- Integral equations --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Group theory --- Global analysis (Mathematics). --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- 517.1 Mathematical analysis
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