Thin discs and a Morera theorem for CR functions

1997 ◽  
Vol 226 (2) ◽  
pp. 327-334 ◽  
Author(s):  
Alexander Tumanov
Keyword(s):  
Cr Functions ◽  
Morera Theorem

Properties of CR-functions and their restrictions to submanifolds

1991 ◽  
Vol 50 (2) ◽  
pp. 813-816
Author(s):  
Kh. P. Gambaryan
Keyword(s):  
Cr Functions

CR structures with group action and extendability of CR functions

1985 ◽  
Vol 82 (2) ◽  
pp. 359-396 ◽  
Author(s):  
M. S. Baouendi ◽  
Linda Preiss Rothschild ◽  
E. Treves
Keyword(s):  
Group Action ◽  
Cr Functions ◽  
Cr Structures

scholarly journals Microlocal hypo-analyticity and extension of CR functions

1983 ◽  
Vol 18 (3) ◽  
pp. 331-391 ◽  
Author(s):  
M. S. Baouendi ◽  
C. H. Chang ◽  
F. Trèves
Keyword(s):  
Cr Functions ◽  
Extension Of Cr Functions

scholarly journals Quaternionic G-Monogenic Mappings in Em

2018 ◽  
Vol 12 ◽  
pp. 1-34
Author(s):  
Vitalii S. Shpakivskyi ◽  
Tetyana S. Kuzmenko
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Complex Variable ◽  
Analytic Functions ◽  
Integral Formula ◽  
Cauchy Integral Formula ◽  
Cauchy Integral ◽  
Partial Differential ◽  
Morera Theorem ◽  
Classical Integral

We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory of the complex variable (the surface and the curvilinear Cauchy integral theorems,the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions.Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiablein the sense of Hausdorff) quaternionic mappings.

scholarly journals Removable singularities of CR functions on singular boundaries

2002 ◽  
Vol 242 (3) ◽  
pp. 491-515 ◽  
Author(s):  
A. Kytmanov ◽  
S. Myslivets ◽  
N. Tarkhanov
Keyword(s):  
Cr Functions ◽  
Removable Singularities

A Remark on Extensions of CR Functions from Hyperplanes

2008 ◽  
Vol 51 (1) ◽  
pp. 21-25
Author(s):  
Luca Baracco
Keyword(s):  
Radon Transform ◽  
Integral Geometry ◽  
Holomorphic Functions ◽  
Holomorphic Extension ◽  
General Statement ◽  
Cr Geometry ◽  
Cr Functions ◽  
Natural Context ◽  
Extension Of Functions

AbstractIn the characterization of the range of the Radon transform, one encounters the problem of the holomorphic extension of functions defined on ℝ2 \ Δℝ (where Δℝ is the diagonal in ℝ2) and which extend as “separately holomorphic” functions of their two arguments. In particular, these functions extend in fact to ℂ2 \ Δℂ where Δℂ is the complexification of Δℝ. We take this theorem from the integral geometry and put it in the more natural context of the CR geometry where it accepts an easier proof and amore general statement. In this new setting it becomes a variant of the celebrated “edge of the wedge” theorem of Ajrapetyan and Henkin.

scholarly journals An edge-of-the-wedge theorem for hypersurface CR functions

2001 ◽  
Vol 11 (4) ◽  
pp. 589-602 ◽  
Author(s):  
Michael G. Eastwood ◽  
C. Robin Graham
Keyword(s):  
Cr Functions
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