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Harmonic analysis --- Fourier series --- Fourier transform --- Banach algebra(Commutative-)
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Mathematics --- Banach algebra --- complex analysis --- frame and wavelet theory --- functional analysis and operator theory --- fuzzy analysis --- nonlinear analysis --- Math --- Science --- Mathematical Theory --- banach algebra --- Mathematics.
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Banach [Algebra's van ] --- Banach [Algebres de ] --- Banach algebras --- Fonctions holomorphes --- Holomorfe functies --- Holomorphic functions --- Banach algebras. --- Holomorphic functions.
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Functional analysis --- Algebra --- Study and teaching. --- Àlgebres de Banach --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Anells normats --- Àlgebres topològiques --- Espais de Banach --- Àlgebres de funcions --- Àlgebres de Von Neumann --- Anàlisi harmònica --- C*-àlgebres --- Mòduls de Banach (Àlgebra)
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Functional analysis --- Banach [Algebra's van ] --- Banach [Algebres de ] --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach algebras --- Banach spaces --- Banach spaces. --- Ideals (Algebra) --- Approximation theory. --- 51 --- Approximation theory --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Algebraic ideals --- Algebraic fields --- Rings (Algebra) --- Functions of complex variables --- Generalized spaces --- Topology --- Mathematics --- 51 Mathematics
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Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Anells (Àlgebra) --- Monoides --- Mòduls (Àlgebra) --- Sistemes modulars (Àlgebra) --- Anells artinians --- Mòduls de Banach (Àlgebra) --- Mòduls de Cohen-Macaulay --- Mòduls injectius (Àlgebra) --- Mòduls projectius (Àlgebra) --- Teoria de divisors --- Teoria de torsió (Àlgebra) --- Grups finits --- Semigrups --- Anells algebraics --- Anells algèbrics --- Àlgebres no associatives --- Àlgebres topològiques --- Anells associatius --- Anells commutatius --- Anells de grup --- Anells no commutatius --- Ideals (Àlgebra) --- Representacions d'anells (Àlgebra) --- Teoria de la mesura
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This book provides an in-depth analysis of selected methods in signal and system theory with applications to problems in communications, stochastic processes and optimal filter theory. The authors take a consistent functional analysis and operator theoretic approach to linear system theory, using Banach algebra and Hardy space techniques. The themes connecting all the chapters are questions concerning the consequences of the causality constraint, which is necessary in all realizable systems, and the question of robustness of linear systems with respect to errors in the data. The first part of the book contains basic background on the necessary mathematical tools and provides a basic foundation of signal and system theory. Emphasis is given to the close relation between properties of linear systems such as causality, time-invariance, and robustness on the one hand and the algebraic structures and analytic properties of the mathematical objects, such as Banach algebras or Hardy spaces, on the other hand. The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz projection and the Hilbert transform. These operations are studied in detail in part two. Part three relates the mathematical techniques that are developed in the first two parts to the behaviour of linear systems that are of interest from an engineering perspective, such as expansions of transfer functions in orthonormal bases, the approximation from measured data and the numerical calculation of the Hilbert transform, as well as spectral factorization.
Signal processing -- Mathematics. --- Signaltheorie -- Hilbert-Transformation -- Banach-Algebra -- Hardy-Raum. --- System theory -- Mathematics. --- Systemtheorie -- Hilbert-Transformation -- Banach-Algebra -- Hardy-Raum. --- Signal processing --- System theory --- Electrical & Computer Engineering --- Electrical Engineering --- Telecommunications --- Engineering & Applied Sciences --- Mathematics --- Communication --- Mathematics. --- Network analysis. --- Network analysis (Communication) --- Engineering. --- Computer organization. --- Computer communication systems. --- Computer engineering. --- Algorithms. --- Applied mathematics. --- Engineering mathematics. --- Electrical engineering. --- Communications Engineering, Networks. --- Computer Engineering. --- Computer Communication Networks. --- Appl.Mathematics/Computational Methods of Engineering. --- Computer Systems Organization and Communication Networks. --- Electric engineering --- Engineering --- Engineering analysis --- Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- Computers --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Organization, Computer --- Electronic digital computers --- Construction --- Industrial arts --- Technology --- Foundations --- Design and construction --- Distributed processing --- Systems, Theory of --- Systems science --- Science --- Methodology --- Philosophy --- Telecommunication. --- Computer network architectures. --- Mathematical and Computational Engineering. --- Architectures, Computer network --- Network architectures, Computer --- Computer architecture --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Information theory --- Telecommuting
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In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional differential topology, and infinite dimensional pointset topology. Later results of the contributors underscore the basic soundness of this selection, which includes survey and expository papers, as well as reports of continuing research.
Topology --- Differential geometry. Global analysis --- Differential topology --- Functional analysis --- Congresses --- Analyse fonctionnnelle --- Geometry, Differential --- Anderson's theorem. --- Annihilator (ring theory). --- Automorphism. --- Baire measure. --- Banach algebra. --- Banach manifold. --- Banach space. --- Bounded operator. --- Cartesian product. --- Characterization (mathematics). --- Cohomology. --- Compact space. --- Complement (set theory). --- Complete metric space. --- Connected space. --- Continuous function. --- Convex set. --- Coset. --- Critical point (mathematics). --- Diagram (category theory). --- Differentiable manifold. --- Differential topology. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dual space. --- Duality (mathematics). --- Endomorphism. --- Equivalence class. --- Euclidean space. --- Existential quantification. --- Explicit formulae (L-function). --- Exponential map (Riemannian geometry). --- Fixed-point theorem. --- Fréchet derivative. --- Fréchet space. --- Fuchsian group. --- Function space. --- Fundamental class. --- Haar measure. --- Hessian matrix. --- Hilbert space. --- Homeomorphism. --- Homology (mathematics). --- Homotopy group. --- Homotopy. --- Inclusion map. --- Infimum and supremum. --- Lebesgue space. --- Lefschetz fixed-point theorem. --- Limit point. --- Linear space (geometry). --- Locally convex topological vector space. --- Loop space. --- Mathematical optimization. --- Measure (mathematics). --- Metric space. --- Module (mathematics). --- Natural topology. --- Neighbourhood (mathematics). --- Normal space. --- Normed vector space. --- Open set. --- Ordinal number. --- Paracompact space. --- Partition of unity. --- Path space. --- Product topology. --- Quantifier (logic). --- Quotient space (linear algebra). --- Quotient space (topology). --- Radon measure. --- Reflexive space. --- Representation theorem. --- Riemannian manifold. --- Schauder fixed point theorem. --- Sign (mathematics). --- Simply connected space. --- Space form. --- Special case. --- Stiefel manifold. --- Strong operator topology. --- Subcategory. --- Submanifold. --- Subset. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topological vector space. --- Topology. --- Transfinite induction. --- Transfinite. --- Transversal (geometry). --- Transversality theorem. --- Tychonoff cube. --- Union (set theory). --- Unit sphere. --- Weak topology. --- Weakly compact. --- Differential topology - Congresses --- Functional analysis - Congresses --- Topology - Congresses --- Analyse fonctionnelle.
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Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.
p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Abelian category. --- Acting in. --- Addition. --- Aisle. --- Algebraic closure. --- Algebraic curve. --- Algebraic structure. --- Algebraic variety. --- Allegory (category theory). --- Analytic function. --- Analytic geometry. --- Analytic space. --- Archimedean property. --- Arithmetic. --- Banach algebra. --- Bertolt Brecht. --- Buttress. --- Centrality. --- Clerestory. --- Commutative diagram. --- Commutative property. --- Complex analysis. --- Contradiction. --- Corollary. --- Cosmetics. --- De Rham cohomology. --- Determinant. --- Diameter. --- Differential form. --- Dimension (vector space). --- Divisor. --- Elaboration. --- Embellishment. --- Equanimity. --- Equivalence class (music). --- Existential quantification. --- Facet (geometry). --- Femininity. --- Finite morphism. --- Formal scheme. --- Fred Astaire. --- Functor. --- Gavel. --- Generic point. --- Geometry. --- Gothic architecture. --- Homomorphism. --- Hypothesis. --- Imagery. --- Injective function. --- Irreducible component. --- Iterated integral. --- Linear combination. --- Logarithm. --- Marni Nixon. --- Masculinity. --- Mathematical induction. --- Mathematics. --- Mestizo. --- Metaphor. --- Morphism. --- Natural number. --- Neighbourhood (mathematics). --- Neuroticism. --- Noetherian. --- Notation. --- One-form. --- Open set. --- P-adic Hodge theory. --- P-adic number. --- Parallel transport. --- Patrick Swayze. --- Phrenology. --- Politics. --- Polynomial. --- Prediction. --- Proportion (architecture). --- Pullback. --- Purely inseparable extension. --- Reims. --- Requirement. --- Residue field. --- Rhomboid. --- Roland Barthes. --- Satire. --- Self-sufficiency. --- Separable extension. --- Sheaf (mathematics). --- Shuffle algebra. --- Subgroup. --- Suggestion. --- Technology. --- Tensor product. --- Theorem. --- Transept. --- Triforium. --- Tubular neighborhood. --- Underpinning. --- Writing. --- Zariski topology.
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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.
Chirurgie (Topologie) --- Heelkunde (Topologie) --- Surgery (Topology) --- Differential topology --- Homotopy equivalences --- Manifolds (Mathematics) --- Topology --- Algebraic topology (object). --- Algebraic topology. --- Ambient isotopy. --- Assembly map. --- Atiyah–Hirzebruch spectral sequence. --- Atiyah–Singer index theorem. --- Automorphism. --- Banach algebra. --- Borsuk–Ulam theorem. --- C*-algebra. --- CW complex. --- Calculation. --- Category of manifolds. --- Characterization (mathematics). --- Chern class. --- Cobordism. --- Codimension. --- Cohomology. --- Compactification (mathematics). --- Conjecture. --- Contact geometry. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dirac operator. --- Disk (mathematics). --- Donaldson theory. --- Duality (mathematics). --- Embedding. --- Epimorphism. --- Excision theorem. --- Exponential map (Riemannian geometry). --- Fiber bundle. --- Fibration. --- Fundamental group. --- Group action. --- Group homomorphism. --- H-cobordism. --- Handle decomposition. --- Handlebody. --- Homeomorphism group. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy extension property. --- Homotopy fiber. --- Homotopy group. --- Homotopy. --- Hypersurface. --- Intersection form (4-manifold). --- Intersection homology. --- Isomorphism class. --- K3 surface. --- L-theory. --- Limit (category theory). --- Manifold. --- Mapping cone (homological algebra). --- Mapping cylinder. --- Mostow rigidity theorem. --- Orthonormal basis. --- Parallelizable manifold. --- Poincaré conjecture. --- Product metric. --- Projection (linear algebra). --- Pushout (category theory). --- Quaternionic projective space. --- Quotient space (topology). --- Resolution of singularities. --- Ricci curvature. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Ring homomorphism. --- Scalar curvature. --- Semisimple algebra. --- Sheaf (mathematics). --- Sign (mathematics). --- Special case. --- Sub"ient. --- Subgroup. --- Submanifold. --- Support (mathematics). --- Surgery exact sequence. --- Surgery obstruction. --- Surgery theory. --- Symplectic geometry. --- Symplectic vector space. --- Theorem. --- Topological conjugacy. --- Topological manifold. --- Topology. --- Transversality (mathematics). --- Transversality theorem. --- Vector bundle. --- Waldhausen category. --- Whitehead torsion. --- Whitney embedding theorem. --- Yamabe invariant.
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