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

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

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

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...

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...

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...

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

natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, namely those for which Δ u ≥ 0 , {\displaystyle...

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

in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions". His work focused on computer science in the last decade of his...

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

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

the mathematical study of harmonic functions, the Perron method, also known as the method of subharmonic functions, is a technique introduced by Oskar...

understanding function behavior. Examples of classes of functions with a rich structure are, in addition to the convex functions, the subharmonic functions and...

rigidity results for functions on complete Riemannian manifolds. A particularly famous result of his says that a subharmonic function cannot be both positive...

{\displaystyle n\geq 2} ) is a polar set if there is a non-constant subharmonic function u {\displaystyle u} on R n {\displaystyle \mathbb {R} ^{n}} such...

using the Perron method, which relies on the maximum principle for subharmonic functions. This approach is described in many text books. It is not well-suited...

harmonic function, by allowing the definition of a function which is 'harmonic at infinity'. This technique is also used in the study of subharmonic and superharmonic...

interest in potential theory because Iαμ is then a (continuous) subharmonic function off the support of μ, and is lower semicontinuous on all of Rn. Consideration...

Research Problems in Function Theory, London: Athlone Press, pp. vii+56. Hayman, W. K.; Kennedy, P. B. (1976), Subharmonic functions. Volume 1, London Mathematical...

the function f r ( z ) = f ( r z ) . {\displaystyle f_{r}(z)=f(rz).} The inequalities can also be deduced, following Riesz (1925), using subharmonic functions...

Times, November 3, 2009. Cunzer, Ela-Chaim (1937). On convex and subharmonic functions (Catalog entry for translated manuscript). Translated by Wlordarski...

martingales correspond to harmonic functions, supermartingales to superharmonic functions, and submartingales to subharmonic functions. Quoted from Snell's Obituary...

Ortega-Cerda', Joaquim; Tilli, Paolo (2022). "A monotonicity theorem for subharmonic functions on manifolds". arXiv:2212.14008 [math.CA]. Video of a lecture by...

1934 he studied subharmonic functions, building on the work of Riesz. Samary Aleksandrovich Galpern. I. I. Privalov, Subharmonic Functions, GITTL, Moscow...

{R} ^{n}} , the coarsest topology making all subharmonic functions (equivalently all superharmonic functions) continuous. Finer topology If X is a set,...

 93. Retrieved 14 April 2011. Boswell, George W. "The Neutral Tone as a Function of Folk-Song Text", Yearbook of the International Folk Music Council, vol...

kind of "complex convexity" remains, namely the fact that z → |z|q is subharmonic for every q > 0. As a consequence, if F ( z ) = ∑ n = 0 + ∞ c n z n ...

important contribution was his work in function theory, in particular Nevanlinna theory and the growth of subharmonic functions. Vorlesungen über Funktionentheorie...

Peter; Schoen, Richard (1984). "Lp and mean value properties of subharmonic functions on Riemannian manifolds". Acta Mathematica. 153 (3–4): 279–301....