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Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes ...

Let G be an open subset of the complex plane C, and let L_a^2(G) denote the collection of all analytic functions f:G->C whose complex modulus is square integrable with ...

Complex Analysis

A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

Let A be a commutative complex Banach algebra. The space of all characters on A is called the maximal ideal space (or character space) of A. This space equipped with the ...

A complex polynomial is a polynomial with complex coefficients.

A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...