• 제목/요약/키워드: hypercomplex system

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Lévy Khinchin Formula on Commutative Hypercomplex System

  • Zabel, Ahmed Moustfa;Dehaish, Buthinah Abdullateef Bin
    • Kyungpook Mathematical Journal
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    • 제48권4호
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    • pp.559-575
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    • 2008
  • A commutative hypercomplex system $L_1$(Q,m) is, roughly speaking, a space which is defined by a structure measure (c(A,B, r), (A,$B{\in}{\beta}$(Q)). Such space has bee studied by Berezanskii and Krein. Our main purpose is to establish a generalization of convolution semigroups and to discuss the role of the L$\'{e}$vy measure in the L$\'{e}$vy-Khinchin representation in terms of continuous negative definite functions on the dual hypercomplex system.

Negative Definite Functions on Hypercomplex Systems

  • Zabel, Ahmed M.;Dehaish, Buthinah A. Bin
    • Kyungpook Mathematical Journal
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    • 제46권2호
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    • pp.285-295
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    • 2006
  • We present a concept of negative definite functions on a commutative normal hypercomplex system $L_1$(Q, $m$) with basis unity. Negative definite functions were studied in [5] and [4] for commutative groups and semigroups respectively. The definition of such functions on Q is a natural generalization of that defined on a commutative hypergroups.

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COSET OF A HYPERCOMPLEX NUMBER SYSTEM IN CLIFFORD ANALYSIS

  • KIM, JI EUN;SHON, KWANG HO
    • 대한수학회보
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    • 제52권5호
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    • pp.1721-1728
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    • 2015
  • We give certain properties of elements in a coset group with hypercomplex numbers and research a monogenic function and a Clifford regular function with values in a coset group by defining differential operators. We give properties of those functions and a power of elements in a coset group with hypercomplex numbers.

CONSTRUCTION OF AN EIGHT DIMENSIONAL NONALTERNATIVE, NONCOMMUTATIVE ALGEBRA

  • Youngkwon Song
    • 충청수학회지
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    • 제36권4호
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    • pp.255-265
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    • 2023
  • The purpose of this article is to construct a unital 8 dimensional hypercomplex number system H*8 that is neither alternative nor commutative unlike the octonions by means of the unital 4 dimensional, commutative, and nonassociative hypercomplex number system H*. We also establish some algebraic properties related to H*8 and compare to those of octonions.

DIFFERENTIALS OF THE BICOMPLEX FUNCTIONS FOR EACH CONJUGATIONS BY THE NAIVE APPROACH

  • Kang, Han Ul;Kim, Min Ji;Shon, Kwang Ho
    • 호남수학학술지
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    • 제39권2호
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    • pp.307-315
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    • 2017
  • In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.