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Analytic continuation gives an equivalence relation between function elements, and the equivalence classes induced by this relation are called global analytic functions.

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

The equations defined by q^. = (partialH)/(partialp) (1) p^. = -(partialH)/(partialq), (2) where p^.=dp/dt and q^.=dq/dt is fluxion notation and H is the so-called ...

If 0<p<infty, then the Hardy space H^p(D) is the class of functions holomorphic on the disk D and satisfying the growth condition ...

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

The nontrivial zeros of the Riemann zeta function correspond to the eigenvalues of some Hermitian operator (Derbyshire 2004, pp. 277-278).

Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...

The bifurcation of a fixed point to a limit cycle (Tabor 1989).

Hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite iff |x|<n ...

The imaginary part I[z] of a complex number z=x+iy is the real number multiplying i, so I[x+iy]=y. In terms of z itself, I[z]=(z-z^_)/(2i), where z^_ is the complex conjugate ...