Generalization of Fueter's result to
- Volume: 8, Issue: 2, page 111-117
- ISSN: 1120-6330
Access Full Article
top
Abstract
topHow to cite
topQian, Tao. "Generalization of Fueter's result to \( \mathbb{R}^{n+1} \)." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.2 (1997): 111-117. <http://eudml.org/doc/244304>.
@article{Qian1997,
abstract = {Fueter's result (see [6,8]) on inducing quaternionic regular functions from holomorphic functions of a complex variable is extended to Euclidean spaces \( \mathbb\{R\}^\{n+1\} \). It is then proved to be consistent with M. Sce's generalization for \( n \) being odd integers [6].},
author = {Qian, Tao},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Clifford analysis; Harmonic analysis; Complex analysis; Singular integrals; Fourier multiplier; Fueter's mapping},
language = {eng},
month = {7},
number = {2},
pages = {111-117},
publisher = {Accademia Nazionale dei Lincei},
title = {Generalization of Fueter's result to \( \mathbb\{R\}^\{n+1\} \)},
url = {http://eudml.org/doc/244304},
volume = {8},
year = {1997},
}
TY - JOUR
AU - Qian, Tao
TI - Generalization of Fueter's result to \( \mathbb{R}^{n+1} \)
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/7//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 2
SP - 111
EP - 117
AB - Fueter's result (see [6,8]) on inducing quaternionic regular functions from holomorphic functions of a complex variable is extended to Euclidean spaces \( \mathbb{R}^{n+1} \). It is then proved to be consistent with M. Sce's generalization for \( n \) being odd integers [6].
LA - eng
KW - Clifford analysis; Harmonic analysis; Complex analysis; Singular integrals; Fourier multiplier; Fueter's mapping
UR - http://eudml.org/doc/244304
ER -
References
top- DELANGHE, R. - SOMMEN, F. - SOUCEK, V., Clifford algebra and spinor valued functions: A function theory for Dirac operator. Kluwer, Dordrecht1992. Zbl0747.53001MR1169463DOI10.1007/978-94-011-2922-0
- MCINTOSH, A. - QIAN, T. - RYAN, J., Spherical convolution operators on star-shaped Lipschitz surfaces. In preparation.
- PEETRE, J. - QIAN, T., Möbius covariance of iterated Dirac operators. J. Austral. Math. Soc., Series A, 56, 1994, 1-12. Zbl1043.31500MR1271529
- QIAN, T., Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space. Preprint. Zbl0921.42012MR1619732DOI10.1007/s002080050162
- RINEHART, R. F., Elements of a theory of intrinsic functions on algebras. Duke Math. J., 32, 1965, 1-19. Zbl0095.28103MR120349
- SCE, M., Osservazioni sulle serie di potenze nei moduli quadratici. Atti Acc. Lincei Rend. fis., s. 8, 23, 1957, 220-225. Zbl0084.28302MR97386
- STEIN, E. M., Singular integrals and differentiability properties of functions. Princeton University Press, 1970. Zbl0207.13501MR290095
- SUDBERY, A., Quaternionic analysis. Math. Proc. Camb. Phil. Soc., 85, 1979, 199-225. Zbl0399.30038MR516081DOI10.1017/S0305004100055638
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.