Negative Definite Functions on Hypercomplex Systems

  • Zabel, Ahmed M. (Mathematics Department, Faculty of Science, Al-Azhar University) ;
  • Dehaish, Buthinah A. Bin (Mathematics Department, Girl's College of Education)
  • 투고 : 2004.11.30
  • 발행 : 2006.06.23

초록

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.

키워드

참고문헌

  1. Ju. M. Berezanskii and A. A. Kalyuzhnyi, Harmonic Analysis in Hypercomplex Systems, Kive, Naukova Dumka, 1992.
  2. Ju. M. Berezanskii and A. A. Kalyuzhnyi, Hypercomplex systems and hypergroups: Connections and distributions, Contemporary Mathematics, 183(1995), 21-44. https://doi.org/10.1090/conm/183/02052
  3. Ju. M. Berezanskii, A. A. Kalyuzhnyi and Ju. G. Kondratiev, Spectral Methods in Infinite Dimensional Analysis, Kluwer Academic Publishers, Netherlands, Vol. 1, 1995.
  4. C. Berg, J. P. R. Christensen and P. Ressel, Harmonic Analysis on Semigroups, Springer-Verlage, Berlin, Heidelberg, New York, 1980.
  5. C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups, Springer-Verlage, Berlin, Heidelberg, 1975.
  6. W. R. Bloom and P. Ressel, Positive definite and related functions on hypergroups, Canad. J. Math., 43(2)(1991), 242-254. https://doi.org/10.4153/CJM-1991-013-2
  7. J. Delsrate, Sur une extension de la formula de Taylor, J. Math. Pures et Appl., 17(3)(1938), 213-231.
  8. J. Delsrate, Hypergroups et operateuers de permutation et de transmutation, in: Colloques Internat. Nacy, 1956, 29-44.
  9. P. Halmos, Measure Theory, van Nostrand, 1950.
  10. A. A. Kalyuzhnyi, A theorem on the existence of multiplicative measure, Ukr. Math. Zh., 35(3)(1983), 369-371.
  11. B. M. Levitan, Generalized of shift operation in connection with almost periodic functions, Mat. Sb., 7(3)(1940), 449-478.
  12. B. M. Levitan, Theory of Generalized Translation Operators, Nauka, Moscow, 1973.