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A path in the complex plane over which contour integration is performed to compute a contour integral. When choosing a contour to evaluate an integral on the real line, a ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a+bsqrt(-d). Here, a and b are half-integers, except for ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

A power series in a variable z is an infinite sum of the form sum_(i=0)^inftya_iz^i, where a_i are integers, real numbers, complex numbers, or any other quantities of a given ...

An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...

Let K be a T2-topological space and let F be the space of all bounded complex-valued continuous functions defined on K. The supremum norm is the norm defined on F by ...