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An analytic function f(z) satisfying the irreducible algebraic equation A_0(z)f^k+A_1(z)f^(k-1)+...+A_k(z)=0 with single-valued meromorphic functions A_j(z) in a complex ...

A Bergman kernel is a function of a complex variable with the "reproducing kernel" property defined for any domain in which there exist nonzero analytic functions of class ...

Let h be a real-valued harmonic function on a bounded domain Omega, then the Dirichlet energy is defined as int_Omega|del h|^2dx, where del is the gradient.

A map u:R^n->R^n from a domain G is called a map of class C^r if each component of u(x)=(u_1(x_1,...,x_n),...,u_m(x_1,...,x_n)) is of class C^r (0<=r<=infty or r=omega) in G, ...

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

Consider a probability space specified by the triple (S,S,P), where (S,S) is a measurable space, with S the domain and S is its measurable subsets, and P is a measure on S ...

If f is analytic on a domain U, then a point z_0 on the boundary partialU is called regular if f extends to be an analytic function on an open set containing U and also the ...

Given a function f specified by parametric variables u_1, ..., u_n, a reparameterization f^^ of f over domain U is a change of variables u_i in U->v_i->V via a function phi ...

A set function is a function whose domain is a collection of sets. In many instances in real analysis, a set function is a function which associates an affinely extended real ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...