scholarly journals On some inequalities in holomorphic function theory in polydisk related to diagonal mapping

2010 ◽  
Vol 60 (2) ◽  
pp. 351-370
Author(s):  
Romi F. Shamoyan ◽  
Olivera R. Mihić
Keyword(s):  
Holomorphic Function ◽  
Function Theory ◽  
Diagonal Mapping

scholarly journals On the Relation between a Cluster set Introduced by Constantinescu and Cornea, and the Fine Cluster set of Cartan, Brelot, and Naïm

1965 ◽  
Vol 8 (1) ◽  
pp. 59-71
Author(s):  
H. L. Jackson
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Limit Theorems ◽  
Function Theory ◽  
Angular Limit ◽  
Boundary Limit ◽  
Cluster Set ◽  
Almost Everywhere ◽  
Bounded Holomorphic Function ◽  
Bounded Holomorphic

The field of boundary limit theorems in analytic function theory is usually considered to have begun about 1906, with the publication of Fatou's thesis [8]. In this remarkable memoir a theorem is proved, that now bears the author's name, which implies that any bounded holomorphic function defined on the unit disk possesses an angular limit almost everywhere (Lebesgue measure) on the frontier. Outstanding classical contributions to this field can be attributed to F. and M. Riesz, R. Nevanlinna, Lusin, Privaloff, Frostman, Plessner, and others.

The Lindelöf principle in ℂn

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Peter Dovbush
Keyword(s):  
Holomorphic Function ◽  
Bounded Domain ◽  
Lipschitz Condition ◽  
Function Theory ◽  
Riemann Sphere ◽  
Normal Function ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Kobayashi Metric ◽  
Lindelöf Principle

AbstractLet D be a bounded domain in ℂn. A holomorphic function f: D → ℂ is called normal function if f satisfies a Lipschitz condition with respect to the Kobayashi metric on D and the spherical metric on the Riemann sphere ̅ℂ. We formulate and prove a few Lindelöf principles in the function theory of several complex variables.

scholarly journals Integral theorems for the quaternionic G-monogenic mappings

2016 ◽  
Vol 24 (2) ◽  
pp. 271-281 ◽  
Author(s):  
V. S. Shpakivskyi ◽  
T. S. Kuzmenko
Keyword(s):  
Holomorphic Function ◽  
Function Theory ◽  
Integral Formula ◽  
Cauchy Integral Formula ◽  
Cauchy Integral ◽  
New Class ◽  
Classical Integral

Abstract In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for G-monogenic mappings.

scholarly journals Certain aspects of holomorphic function theory on some genus-zero arithmetic groups

2016 ◽  
Vol 19 (2) ◽  
pp. 360-381 ◽  
Author(s):  
Jay Jorgenson ◽  
Lejla Smajlović ◽  
Holger Then
Keyword(s):  
Holomorphic Function ◽  
Present Article ◽  
Cusp Form ◽  
Modular Forms ◽  
Discrete Group ◽  
Function Theory ◽  
Arithmetic Groups ◽  
Genus Zero ◽  
Free Level ◽  
Holomorphic Modular Forms

There are a number of fundamental results in the study of holomorphic function theory associated to the discrete group $\operatorname{PSL}(2,\mathbb{Z})$, including the following statements: the ring of holomorphic modular forms is generated by the holomorphic Eisenstein series of weights four and six, denoted by $E_{4}$ and $E_{6}$; the smallest-weight cusp form $\unicode[STIX]{x1D6E5}$ has weight twelve and can be written as a polynomial in $E_{4}$ and $E_{6}$; and the Hauptmodul $j$ can be written as a multiple of $E_{4}^{3}$ divided by $\unicode[STIX]{x1D6E5}$. The goal of the present article is to seek generalizations of these results to some other genus-zero arithmetic groups $\unicode[STIX]{x1D6E4}_{0}(N)^{+}$ with square-free level $N$, which are related to ‘Monstrous moonshine conjectures’. Certain aspects of our results are generated from extensive computer analysis; as a result, many of the space-consuming results are made available on a publicly accessible web site. However, we do present in this article specific results for certain low-level groups.

The Diagonal Mapping in Bmoa-Type Spaces of Analytic Functions on the Polydisk

2009 ◽  
Vol 16 (3) ◽  
pp. 561-574
Author(s):  
Romi F. Shamoyan
Keyword(s):  
Holomorphic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Unit Disc ◽  
Diagonal Mapping ◽  
Type Spaces ◽  
Unit Polydisk ◽  
Spaces Of Analytic Functions

Abstract For any holomorphic function 𝑓 on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag 𝑓(𝑧) = 𝑓(𝑧, . . . , 𝑧) and prove that the diagonal map Diag maps the space of the polydisk onto the space of the unit disk.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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