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In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory. Intuitively, subharmonic functions are related to convex functions of one variable as follows.
One can see that at some parameter values and initial conditions, the system’s oscillation spectrum is heavily contributed (almost dominated) by the \(3^{\text {rd }}\) subharmonic, i.e. the Fourier component of frequency \(\omega / 3 \approx \omega_{0}\).
In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways.
That is, f is harmonic on every complex line. A function f: U → R ∪ { − ∞} is plurisubharmonic, sometimes plush or psh for short, if it is upper-semicontinuous and for every a, b ∈ Cn, the function of one variable ξ ↦ f(a + bξ) is subharmonic (whenever a + bξ ∈ U ).
23 de ene. de 2021 · Subharmonic function. A function $ u = u ( x): D \rightarrow [ - \infty , \infty ) $ of the points $ x = ( x _ {1} \dots x _ {n} ) $ of a Euclidean space $ \mathbf R ^ {n} $, $ n \geq 2 $, defined in a domain $ D \subset \mathbf R ^ {n} $ and possessing the following properties: 1) $ u ( x) $ is upper semi-continuous in $ D $; 2) for ...
Definición de subharmonic del Collins Diccionario inglés. Read about the team of authors behind Collins Dictionaries. Noticias de Collins Desafío exprés. Resultado. Pregunta 1 - Puntuación: 0 / 5. BIRDS. Drag the correct answer into the box. starling. blackbird. heron.
8 de sept. de 2019 · A chapter from a book series on function theory, covering topics such as mean value properties, Harnack principle, null quadrature domains, and fine topology. Includes problems, solutions, and references for further reading.
