Sentence examples for be the subharmonic function from inspiring English sources

Then (-u(x)) will be the subharmonic function and (-u_{h}(x)) will approximate (-u(x)).

Based on the elaborate research, Yoshida ([17] and [18]) has considered the subharmonic function defined on a cone or a cylinder which is dominated on the boundary by a certain function and generalized the classical Phragmén-Lindelöf theorem by making a harmonic majorant.

The most widely known is the subharmonic route, which is characterized by an increasing number of subharmonics of the driving frequency.

Let (0< r< R) and (u t,Phi)) be a subharmonic function on (mathfrak{C}_{n}(Gamma;(r,R))).

Let u be a subharmonic function in (overline {mathfrak{C}_{n}(Gamma)}) such that (u'=u|partial{mathfrak{C}_{n}(Gamma)}) satisfies (1.5).

The subharmonic functions exhibit many properties of convex functions.

Let (mathrm{SH}(Omega )) denote the subharmonic functions on a domain (Omega subset {mathbb C}).

The subharmonic functions attain their maximum and superharmonic functions attain their minimum on the boundary (see e.g. Evans Section 6.4 [2]).

Let g be a nonnegative lower semi-continuous function on (partial{mathfrak{C}_{n}(Gamma)}) satisfying (1.5) and u be a nonnegative subharmonic function on (mathfrak{C}_{n}(Gamma )) such that limsup_{Pinmathfrak{C}_{n}(Gamma), Prightarrow Q}u P leq g(Q) (3.7) for any (Qinpartial{mathfrak{C}_{n}(Gamma)}).

Let u be a nonnegative subharmonic function on (mathfrak{C}_{n}(Gamma)) satisfying (1.4) for any (Qin partial{mathfrak{C}_{n}(Gamma)}) and mathscr{U}_{u^< +infty.

The natural generalization of convex functions for n variables is a subharmonic function and similarly of concave functions it is a superharmonic function.