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Everything about Holomorphic function
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex derivative in a neighbourhood is a very strong condition: It implies that a holomorphic function is infinitely differentiable and locally equal to its own Taylor series. Holomorphic functions are the central objects of study in complex analysis. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Holomorphic functionA 5-minute orientation
- Skim a recent paper: Finite element/holomorphic operator function method for the transmission eigenvalue problemInfluential work since 2022
- Pick up a classic book: Leçons sur les fonctions entièresThe most-reprinted book on the subject
- Read the landmark paper: Holomorphic wave function of the UniverseCited 181 times
- Go sideways: Cauchy–Riemann equationsA closely related topic
- Go sideways: Complex analysisA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Holomorphic wave function of the Universe
Stable rank in holomorphic function algebras
The Bergman Kernel Function and Propert Holomorphic Mappings
The holomorphic flow of the Riemann zeta function
Holomorphic function spaces on the Hartogs triangle
Holomorphic Convexity for General Function Algebras
HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES
On holomorphic operator function equations
🆕 Influential since 2022
Finite element/holomorphic operator function method for the transmission eigenvalue problem
A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves
FE-holomorphic operator function method for nonlinear plate vibrations with elastically added masses
A new family of holomorphic homogeneous regular domains and some questions on the squeezing function
Daugavet property of Banach algebras of holomorphic functions and norm-attaining holomorphic functions
📚 Books worth reading
Leçons sur les fonctions entièresEmile Borel · 1900
Extension of holomorphic functionsMarek Jarnicki · 2000
Stein manifolds and holomorphic mappingsFranc Forstnerič · 2011- 📕Handbook of Analytic Operator TheoryKehe Zhu · 2019
- 📕Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)Elias M. Stein · 2015
- 📕Holomorphic Functions of Several VariablesLudger Kaup, Burchard Kaup · 1983
Slice Hyperholomorphic Schur AnalysisDaniel Alpay, Fabrizio Colombo · 2016
Holomorphic functions, domains of holomorphy and local propertiesLeopoldo Nachbin · 1970
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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