In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex...

hold, although other properties of harmonic functions may fail. More generally, a function is subharmonic if and only if, in the interior of any ball...

Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. However, unlike subharmonic functions (which are defined on a Riemannian...

potential theory, a subharmonic function f satisfies Δf ≥ 0. Any subharmonic function that is bounded above by a harmonic function for all points on the...

discrete Laplace operator. Similar to continuous subharmonic functions one can define subharmonic functions for finite-difference approximations u h {\displaystyle...

of the ball (mean value property). Also subharmonic function and superharmonic function. Elementary function: composition of arithmetic operations, exponentials...

condition than a holomorphically convex. The subharmonic function looks like a kind of convex function, so it was named by Levi as a pseudoconvex domain...

Bloch space, Bergman space and Sobolev space. Subharmonic function – Class of mathematical functions Kellogg's theorem Garabedian, P. R.; Schiffer, M...

sets), convex functions (on vector and affine spaces), harmonic and subharmonic functions (on Riemannian manifolds), analytic functions (usually of one...

whether function spaces other than the negative subharmonic functions are degenerate, e.g. Riemann surfaces on which all bounded holomorphic functions are...