Search Results for ""

Let gamma be a path given parametrically by sigma(t). Let s denote arc length from the initial point. Then int_gammaf(s)ds = int_a^bf(sigma(t))|sigma^'(t)|dt (1) = ...

The interval (generally, the smallest interval) over which the values of a periodic function recur. Functions may have one or more periods over time and in space.

An upper semicontinuous function whose restrictions to all complex lines are subharmonic (where defined). These functions were introduced by P. Lelong and Oka in the early ...

Let f:R->R, then the positive part of f is the function f^+:R->R defined by f^+(x)=max(f(x),0) The positive part satisfies the identity f=f^+-f^-, where f^- is the negative ...

Let C^omega(I) be the set of real analytic functions on I. Then C^omega(I) is a subalgebra of C^infty(I). A necessary and sufficient condition for a function f in C^infty(I) ...

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

The rectifiable sets include the image of any Lipschitz function f from planar domains into R^3. The full set is obtained by allowing arbitrary measurable subsets of ...

The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that lim_(n->infty)int_a^bK(lambda,z)Csin(nz)dz=0 (1) for arbitrarily large C and "nice" ...

Find an analytic parameterization of the compact Riemann surfaces in a fixed homeomorphism class. The Ahlfors-Bers theorem proved that Riemann's moduli space gives the ...