Extension results for slice regular functions of a quaternionic variable
In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function f at a point q = x + y I can be recovered by the values of f at the points q + y J and q + y K for any choice of imaginary units I , J , K . This result allows us t...
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| Vydané v: | Advances in mathematics (New York. 1965) Ročník 222; číslo 5; s. 1793 - 1808 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Inc
01.12.2009
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| Predmet: | |
| ISSN: | 0001-8708, 1090-2082 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function
f at a point
q
=
x
+
y
I
can be recovered by the values of
f at the points
q
+
y
J
and
q
+
y
K
for any choice of imaginary units
I
,
J
,
K
. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains, called axially symmetric domains. We show, in particular, that axially symmetric domains play, for slice regular functions, the role played by domains of holomorphy for holomorphic functions. |
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| ISSN: | 0001-8708 1090-2082 |
| DOI: | 10.1016/j.aim.2009.06.015 |