several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators), named after Wilhelm Wirtinger who introduced them in 1927...

Wilhelm Wirtinger (19 July 1865 – 16 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups...

the same way that a normal derivative describes how a function is approximated by a linear map. The Wirtinger derivatives are a set of differential operators...

Holomorphic separability Meromorphic function Quadrature domains Wirtinger derivatives The original French terms were holomorphe and méromorphe. Lorsqu'une...

of a square root Hermitian function – Type of complex function Wirtinger derivatives – Concept in complex analysis Friedberg, Stephen; Insel, Arnold;...

x {\displaystyle x} and y {\displaystyle y} . Defining the two Wirtinger derivatives as ∂ ∂ z = 1 2 ( ∂ ∂ x − i ∂ ∂ y ) , ∂ ∂ z ¯ = 1 2 ( ∂ ∂ x + i ∂...

are tangent vectors Kähler differential Hasse derivative p-derivation Wirtinger derivatives Derivative of the exponential map Bourbaki, Nicolas (1989)...

isoperimetric inequality to the function's level sets. In one dimension, this is Wirtinger's inequality for functions. However, in some special cases the constant...

be a function of two real variables x and y. Use is made of the Wirtinger derivatives, which are partial differential operators: ∂ ∂ z = 1 2 ( ∂ ∂ x −...

/ ∂ z ¯ {\displaystyle \partial /\partial {\overline {z}}} are Wirtinger derivatives. Classically this differential equation was used by Gauss to prove...

y_{i}}}=-{\frac {\partial v}{\partial x_{i}}}} Using the formalism of Wirtinger derivatives, this can be reformulated as : ∀ i ∈ { 1 , … , n } , ∂ f ∂ z i ¯...

other inequalities named after Wirtinger, see Wirtinger's inequality. In the mathematical field of analysis, the Wirtinger inequality is an important inequality...

{1}{2}}iu={\frac {\partial \psi }{\partial {\bar {z}}}}} (using the Wirtinger derivatives). This is calculated to be equal to 1 2 i u = f ( z ) + z f ′ ¯...

]}^{*}S(f)+G(f)G^{*}(f)N(f)} To find the minimum error value, we calculate the Wirtinger derivative with respect to   G ( f ) {\displaystyle \ G(f)} and set it equal...

( f ( n − 1 ) ) ′ {\displaystyle f^{(n)}=(f^{(n-1)})^{'}} (see Wirtinger derivatives § Relation with complex differentiation). Moreover, taking f ( z...

has been generalized to optimization over complex numbers using Wirtinger derivatives. Xiong, Kai; Zhao, Guanghui; Shi, Guangming; Wang, Yingbin (2019-09-12)...

formula Pompeiu–Hausdorff metric Pompeiu's theorem Pompeiu derivative Wirtinger derivatives Petrașcu Zamfirache, Cosmin (September 22, 2017). "Românul...

the interior of D and continuous on its boundary ∂D. the iterated Wirtinger derivatives of order α of a given complex valued function f ∈ A(D) are expressed...

spaces are equivalent. Friedrichs's inequality generalizes the Poincaré–Wirtinger inequality, which deals with the case k = 1. Let Ω {\displaystyle \Omega...

Levi, following a then well established practice, does not use Wirtinger derivatives. Celli, Andrea; Mattaliano, Maurizio, eds. (2015), Eugenio Elia...

p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing...

does not imply that it is pluriharmonic. Plurisubharmonic function Wirtinger derivatives See for example (Severi 1958, p. 196) and (Rizza 1955, p. 202)....

a motor variable. An approach to D-holomorphic functions using a Wirtinger derivative was given by Motter & Rossa: The function f = u + j v is called D-holomorphic...

inequality Pu's inequality Gromov's inequality for complex projective space Wirtinger inequality (2-forms) Gromov's systolic inequality for essential manifolds...

conditions to be satisfied on the whole boundary of a given domain. M. Wirtinger, dans une conversation privée, a attiré mon attention sur le probleme...

of the 20th century. Important results have been achieved by Wilhelm Wirtinger in 1927. While the above low-level definitions, including the addition...

string. One way to show this is by estimating the energy, which satisfies Wirtinger's inequality: for a function f : [ 0 , 1 ] → C {\displaystyle f:[0,1]\to...

a smooth manifoldPages displaying wikidata descriptions as a fallback Wirtinger inequality (2-forms) – inequality applicable to 2-formsPages displaying...

topology. (This fails completely for real submanifolds.) Explicitly, Wirtinger's formula says that v o l ( Y ) = 1 r ! ∫ Y ω r , {\displaystyle \mathrm...

been reprinted many times, a 1996 paperback has ISBN 0-521-09189-6.) Wirtinger, W. (1905). "Über eine besondere Dirichletsche Reihe". Journal für die...