Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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Existence theorems of an operator-valued feynman integral as an $L(L_1,C_0)$ theory

  • Ahn, Jae-Moon (Department of Mathematics Education, Kun-Kuk University, Seoul 151-742) ;
  • Chang, Kun-Soo (Department of Mathematics, Yonsei University) ;
  • Kim, Jeong-Gyoo (Department of Mathematics and Statistics, University of Nebrasak, Lincoln, NE 68588, U.S.A) ;
  • Ko, Jung-Won (Department of Mathematics and Statistics, University of Nebrasak, Lincoln, NE 68588, U.S.A.) ;
  • Ryu, Kun-Sik (Department of Mathematics, Hannam University, Daejon 330-791)
  • Published : 1997.05.01
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Abstract

The existence of an operator-valued function space integral as an operator on $L_p(R) (1 \leq p \leq 2)$ was established for certain functionals which involved the Labesgue measure [1,2,6,7]. Johnson and Lapidus showed the existence of the integral as an operator on $L_2(R)$ for certain functionals which involved any Borel measures [5]. J. S. Chang and Johnson proved the existence of the integral as an operator from L_1(R)$ to $C_0(R)$ for certain functionals involving some Borel measures [3]. K. S. Chang and K. S. Ryu showed the existence of the integral as an operator from $L_p(R) to L_p'(R)$ for certain functionals involving some Borel measures [4].

Keywords

References

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  2. Nagoya Math. J. v.51 An operator-valued function space integral applied to multiple integral of functions of class L₁ R. H. Cameron
  3. J.Korean Math. Soc. No.1 v.28 The Feynman integral and Feynman’s operational Calculus;$L(L_1(R),C_0(R))$ theory J. S. Chang;G.W. Johnson
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