An Extension Theorem for Biregular Functions in Clifford Analysis

2008 ◽  
pp. 1-9
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem

scholarly journals The Cauchy–Kovalevskaya extension theorem in Hermitian Clifford analysis

2011 ◽  
Vol 381 (2) ◽  
pp. 649-660 ◽  
Author(s):  
F. Brackx ◽  
H. De Schepper ◽  
R. Lávička ◽  
V. Souček
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Hermitian Clifford Analysis

scholarly journals Fischer Decomposition and Cauchy–Kovalevskaya Extension in Fractional Clifford Analysis: The Riemann–Liouville Case

2016 ◽  
Vol 60 (1) ◽  
pp. 251-272 ◽  
Author(s):  
N. Vieira
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Extension Principle ◽  
Homogeneous Polynomials ◽  
Fischer Decomposition ◽  
Spherical Monogenics ◽  
Fueter Polynomials ◽  
Fractional Clifford Analysis ◽  
Extension Of Functions ◽  
Fractional Function

AbstractIn this paper we present the basic tools of a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations via fractional Riemann–Liouville derivatives. A Fischer decomposition, Almansi decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed. Moreover, we establish the fractional Cauchy–Kovalevskaya extension (FCK extension) theorem for fractional monogenic functions defined on ℝd. Based on this extension principle, fractional Fueter polynomials, forming a basis of the space of fractional spherical monogenics, i.e. fractional homogeneous polynomials, are introduced. We study the connection between the FCK extension of functions of the form xPl and the classical Gegenbauer polynomials. Finally, we present an example of an FCK extension.

scholarly journals A Holomorphic Extension Theorem using Clifford Analysis

2009 ◽  
Vol 5 (1) ◽  
pp. 113-130 ◽  
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes ◽  
Dixan Peña Peña ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Holomorphic Extension

scholarly journals The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis

2011 ◽  
Vol 10 (4) ◽  
pp. 1097-1109 ◽  
Author(s):  
Hilde De Ridder ◽  
Hennie Schepper ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Discrete Clifford Analysis

scholarly journals The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis

2010 ◽  
Author(s):  
H. De Ridder ◽  
H. De Schepper ◽  
F. Sommen ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Discrete Clifford Analysis

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

scholarly journals Hopf Extension Theorem of Measure

2009 ◽  
Vol 17 (2) ◽  
Author(s):  
Noboru Endou ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Extension Theorem
Sign in / Sign up

Export Citation Format

Share Document