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continuation theorem

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  • Analytic continuation — In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where …   Wikipedia

  • Monodromy theorem — Illustration of analytic continuation along a curve (only a finite number of the disks Ut are shown) …   Wikipedia

  • Numerical continuation — is a method of computing approximate solutions of a system of parameterized nonlinear equations, The parameter λ is usually a real scalar, and the solution an n vector. For a fixed parameter value λ,, maps Euclidean n space into itself. Often the …   Wikipedia

  • Hartogs' extension theorem — In mathematics, precisely in the theory of functions of several complex variables, Hartogs extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the… …   Wikipedia

  • Edge-of-the-wedge theorem — In mathematics, the edge of the wedge theorem implies that holomorphic functions on two wedges with an edge in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum …   Wikipedia

  • Fundamental theorem of algebra — In mathematics, the fundamental theorem of algebra states that every non constant single variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.Sometimes,… …   Wikipedia

  • Spin-statistics theorem — Statistical mechanics Thermodynamics · …   Wikipedia

  • Open mapping theorem (complex analysis) — In complex analysis, the open mapping theorem states that if U is a connected open subset of the complex plane C and f : U → C is a non constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of… …   Wikipedia

  • Ostrowski–Hadamard gap theorem — In mathematics, the Ostrowski–Hadamard gap theorem is a result about the analytic continuation of complex power series whose non zero terms are of orders that have a suitable gap between them. Such a power series is badly behaved in the sense… …   Wikipedia

  • Séminaire Nicolas Bourbaki (1950–1959) — Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s. 1950/51 series *33 Armand Borel, Sous groupes compacts maximaux des groupes de Lie, d après Cartan, Iwasawa et Mostow (maximal compact subgroups) *34 Henri Cartan, Espaces… …   Wikipedia

  • Séminaire Nicolas Bourbaki (1960–1969) — Continuation of the Séminaire Nicolas Bourbaki programme, for the 1960s.1960/61 series*205 Adrien Douady, Plongements de sphères, d après Mazur et Brown (embeddings of spheres) *206 Roger Godement, Groupes linéaires algébriques sur un corps… …   Wikipedia

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