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The Cauchy-Kowalewski product for bicomplex holomorphic functions

(2012) MATHEMATISCHE NACHRICHTEN. 285(10). p.1230-1242
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Abstract
In this paper we study the Cauchy-Kowalewski extension of real analytic functions satisfying a system of differential equations connected to bicomplex analysis, and we use this extension to study the product in the space of bicomplex holomorphic functions. We also show how these ideas can be used to define a Fourier transform for bicomplex holomorphic functions.
Keywords
35A10, MSC (2010) 30G35, Bicomplex numbers, Cauchy-Kowalewski extension, holomorphicity

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Citation

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Chicago
De Bie, Hendrik, Daniele Struppa, Adrian Vajiac, and Mihaela Vajiac. 2012. “The Cauchy-Kowalewski Product for Bicomplex Holomorphic Functions.” Mathematische Nachrichten 285 (10): 1230–1242.
APA
De Bie, H., Struppa, D., Vajiac, A., & Vajiac, M. (2012). The Cauchy-Kowalewski product for bicomplex holomorphic functions. MATHEMATISCHE NACHRICHTEN, 285(10), 1230–1242.
Vancouver
1.
De Bie H, Struppa D, Vajiac A, Vajiac M. The Cauchy-Kowalewski product for bicomplex holomorphic functions. MATHEMATISCHE NACHRICHTEN. 2012;285(10):1230–42.
MLA
De Bie, Hendrik, Daniele Struppa, Adrian Vajiac, et al. “The Cauchy-Kowalewski Product for Bicomplex Holomorphic Functions.” MATHEMATISCHE NACHRICHTEN 285.10 (2012): 1230–1242. Print.
@article{3032060,
  abstract     = {In this paper we study the Cauchy-Kowalewski extension of real analytic functions satisfying a system of differential equations connected to bicomplex analysis, and we use this extension to study the product in the space of bicomplex holomorphic functions. We also show how these ideas can be used to define a Fourier transform for bicomplex holomorphic functions.},
  author       = {De Bie, Hendrik and Struppa, Daniele and Vajiac, Adrian and Vajiac, Mihaela},
  issn         = {0025-584X},
  journal      = {MATHEMATISCHE NACHRICHTEN},
  keyword      = {35A10,MSC (2010) 30G35,Bicomplex numbers,Cauchy-Kowalewski extension,holomorphicity},
  language     = {eng},
  number       = {10},
  pages        = {1230--1242},
  title        = {The Cauchy-Kowalewski product for bicomplex holomorphic functions},
  url          = {http://dx.doi.org/10.1002/mana.201100047},
  volume       = {285},
  year         = {2012},
}

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