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The continuous image of a Polish space, also called an analytic set.

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity ...

If f(z) is continuous in a region D and satisfies ∮_gammafdz=0 for all closed contours gamma in D, then f(z) is analytic in D. Morera's theorem does not require simple ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

Let f be a bounded analytic function on D(0,1) vanishing to order m>=0 at 0 and let {a_j} be its other zeros, listed with multiplicities. Then ...

A system of linear differential equations (dy)/(dz)=A(z)y, (1) with A(z) an analytic n×n matrix, for which the matrix A(z) is analytic in C^_\{a_1,...,a_N} and has a pole of ...

Let f be analytic on a domain U subset= C, and assume that f never vanishes. Then if there is a point z_0 in U such that |f(z_0)|<=|f(z)| for all z in U, then f is constant. ...