Results 251 to 260 of about 10,326,050 (296)

Zeros of Holomorphic Functions

2007
There are certain (classical families of) functions of a complex variable that mathematicians have studied frequently enough for them to acquire their own names. These are, of course, functions that arise naturally and repeatedly in various mathematical settings. Many of these functions are defined by infinite products. Examples of such named functions
Irwin Kra, Rubí E. Rodríguez, Jane Gilman   +2 more
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Functions Holomorphic in a Disc

1992
For f in H(U) and t in [0, 2π), $$ f*(t)\mathop = \limits^{def} \left\{ {_0^{\lim _{r \uparrow 1} f\left( {re^{it} } \right)} } \right.\,{\text{when}}\,{\text{the limit}}\,{\text{exists}}\,{\text{otherwise}} $$ is the radial limit function. The (Hardy class) $$ \left\{ {f:f \in H(U),_{z \in U}^{\sup \left| {f(z)} \right| < \infty } } \right\}
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Holomorphic functions unbounded on curves of finite length

, 2014
Given a pseudoconvex domain , we prove that there is a holomorphic function f on D such that the lengths of paths $$p:\ [0,1] \rightarrow D$$p:[0,1]→D along which $$\mathfrak {R}f$$Rf is bounded above, with p(0) fixed, grow arbitrarily fast as $$p(1 ...
J. Globevnik
semanticscholar   +1 more source

Function Theory on Symplectic Manifolds

, 2014
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory
L. Polterovich, D. Rosen
semanticscholar   +1 more source

From the holomorphic Wilson loop to ‘d log’ loop-integrands of super-Yang-Mills amplitudes

, 2012
A bstractThe S-matrix for planar $ \mathcal{N} $ = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand
A. Lipstein, L. Mason
semanticscholar   +1 more source

Semigroups of Holomorphic Functions

2020
In this chapter we introduce the primary subject of our study: continuous one-parameter semigroups of holomorphic self-maps of the unit disc. We establish their main basic properties and extend to this context the Denjoy-Wolff Theorem. Then we characterize groups of automorphisms and more generally of linear fractional self-maps of the unit disc.
Filippo Bracci, Santiago Díaz-Madrigal, Manuel D. Contreras   +2 more
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Holomorphic harmonic functions

Russian Journal of Mathematical Physics, 2008
We consider boundary problems for holomorphic harmonic functions on hyperboloids at ℂn using concepts of integral geometry.
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The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function

, 2016
B. Khabibullin, T. Baiguskarov
semanticscholar   +1 more source

Elementary Theory of Holomorphic Functions

1985
In this chapter, we shall develop the classical theory of holomorphic functions. The Looman—Menchoff theorem, proved in §1.6, is less standard than the rest of the material.
Raghavan Narasimhan, Yves Nievergelt
openaire   +2 more sources

Normality Criteria of Meromorphic Functions Sharing a Holomorphic Function

, 2015
D. Meng, P. Hu
semanticscholar   +1 more source