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...for [[Laplace's equation]]. The Perron method works by finding the largest subharmonic function with boundary values below the desired values; the "Perron solutio ...rron solution is defined by taking the pointwise supremum over a family of functions <math>S_\varphi</math>, ...

...al|first1=Wladimir Igorewitsch|last1=Mazaew |title=On the growth of entire functions that admit a certain estimate from below |journal=Soviet Math. Dokl. |volum ...Kheyfits |publisher=Birkhäuser |title=Growth of Schrödingerian Subharmonic Functions Admitting Certain Lower Bounds |encyclopedia=Advances in Harmonic Analysis ...

The theory of holomorphic (=[[analytic function|analytic]]) functions of one complex variable is one of the most beautiful and most useful parts ...maps between two-dimensional spaces ([[Riemann surfaces]]). The theory of functions ...

{{Functions}} ...analysis]]. In particular, many [[function space]]s consist of real-valued functions. ...

...e]] [[composition operator]] on various [[function space]]s of holomorphic functions on the disk. These spaces include the [[Hardy space]]s, the [[Bergman space ...Then the composition operator ''C''_''h'' defined on holomorphic functions ''f'' on ''D'' by ...

*{{cite journal|mr=0094452|last1=Huber|first1=Alfred|title=On subharmonic functions and differential geometry in the large|journal=[[Commentarii Mathematici He ...

{{defn|1=[[Ascoli's theorem]] says that an equicontinous bounded sequence of functions on a compact subset of <math>\mathbb{R}^n</math> has a convergent subsequen {{defn|1=The [[convolution]] <math>f * g</math> of two functions on a convex set is given by ...

...d zero distribution of [[polynomial]]s and entire [[Function (mathematics)|functions]], via [[Correlation inequality|correlation inequalities]] and [[statistica ...from vertex operator theory to zero distribution of polynomials and entire functions, via correlation inequalities and statistical mechanics. His thesis consist ...

...n]]s, supermartingales to superharmonic functions, and submartingales to [[subharmonic function]]s.<ref name=OJLD/>}} ...

...journal |last1=Hofstadter |first1=Douglas R. |title=Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields |journal=Phys ...ny-body systems, phase space crystals study the interplay of the potential subharmonic modes that are arranged periodically in phase space. There is a trend to st ...

...st=E.|year=1991|title=Some integral identities and inequalities for entire functions and their application to the coherent state transform|journal=Journal of Fu ...3=J. |last4=Tilli |first4=P. |title=A monotonicity theorem for subharmonic functions on manifolds |date=2022 |class=math.CA |eprint=2212.14008}}</ref> ...

...ytically, i.e., in terms of well-studied functions such as [[trigonometric functions]]. ...be "integrable" if this final integration can be solved in terms of known functions. ...