scholarly journals On the Schwarz reflection principle

1982 ◽  
Vol 272 (2) ◽  
pp. 711-711
Author(s):  
J. S. Hwang
Keyword(s):  
Reflection Principle ◽  
Schwarz Reflection Principle

scholarly journals Further properties of the Bergman spaces of slice regular functions

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Fabrizio Colombo ◽  
J. Oscar González-Cervantes ◽  
Irene Sabadini
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Half Plane ◽  
Bergman Kernel ◽  
Bergman Spaces ◽  
Reflection Principle ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Complex Half Plane ◽  
Schwarz Reflection Principle

AbstractWe continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.

scholarly journals On the Schwarz reflection principle.

1953 ◽  
Vol 2 (2) ◽  
pp. 151-156 ◽  
Author(s):  
A. J. Lohwater
Keyword(s):  
Reflection Principle ◽  
Schwarz Reflection Principle

scholarly journals Minimal Surfaces with Only Horizontal Symmetries

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Márcio Fabiano da Silva ◽  
Guillermo Antonio Lobos ◽  
Valério Ramos Batista
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Reflection Principle ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic ◽  
Horizontal Type ◽  
Straight Lines ◽  
Schwarz Reflection Principle

The Schwarz reflection principle states that a minimal surface S in ℝ3 is invariant under reflections in the plane of its principal geodesics and also invariant under 180°-rotations about its straight lines. We find new examples of embedded triply periodic minimal surfaces for which such symmetries are all of horizontal type.

The Reflection Principle for Banach Space-Valued Analytic Functions

1969 ◽  
Vol 21 ◽  
pp. 1189-1191
Author(s):  
Mark Finkelstein
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Power Series ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Reflection Principle ◽  
Complex Numbers ◽  
Convergent Power Series ◽  
Regular Subset ◽  
Schwarz Reflection Principle

We give sufficient conditions for the continuation of an analytic function with values in a Branch space. For analytic functions taking complex numbers as values, the principle is known as the Schwarz Reflection Principle.A function defined on a domain of the complex plane with values in a Banach space X is analytic if it possesses at each point Z0 of the domain a convergent power series in z, with coefficients in X.THEOREM. Let D be a domain in the upper half-plane, and E a regular subset of the boundary of D. Suppose that E is an interval of the real axis (a,b). Let f be an analytic function defined on D, continuous up to E, taking values in a Banach space X. Let the image of D under f be Ω, and let Γ be the part of the boundary of Ω which is the image of E under f.

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