DOI QR코드

DOI QR Code

ANALYTIC FUNCTIONS OF k SINGLE INTEGRALS

  • Park, Yeon-Hee (Department of Mathematics Education and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2006.12.07
  • Accepted : 2007.01.22
  • Published : 2007.03.25

Abstract

In this paper we establish the existence theorem of the operator-valued function space integral $K_{\lambda}(F)$ for $\lambda\in\mathbb{C}_{+,\lambda_0}^\sim$ where F is of the form (1.1). Our result is a generalization for Johnson and Skoug result in [8].

Keywords

References

  1. R.P.Boas, Entire functions, Academic Press, New York, 1954.
  2. R.H. Cameron and D.A Storvick, An operator valued function space integral a related integral equation, J. Math, and Mech., 18 (1968), 517-552.
  3. K.S.Chang and K.S.Ryu, Analytic operator valued function space integrals as an L($L_{P},L_{P'}$,) theory, Trans. Amer. Math. Soc., vol. 330, no. 2, (1992), 697-709. https://doi.org/10.2307/2153930
  4. B.A.Fuks, Analytic Functions of several complex variables, A.M.S. Translations of Mathematical Monographs, 8 (1963).
  5. E.Hille and R.S.Phillips, Functional analysis and semi-group, Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc, Providence, R.I., 1957.
  6. G.W.Johnson and M.L.Lapidus, Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman's operational calculus, Mem. Amer. Math. Soc, vol. 62, no. 351, 1986.
  7. G.W.Johnson and M.L.Lapidus, The Feynman integral and Feynman's Operational Calculus, Oxford University Press, New York, 2000.
  8. G.W. Johnson and D.L.Skoug, The Cameron-Storvick function space integral: An $L(L_{P},L_{P'})$ theory, Nagoya Math. J., vol. 60, (1976), 93-137. https://doi.org/10.1017/S0027763000017189
  9. M.Reed and B.Simon, Methods of mathematical physics, Vols. I,II,III, rev. and enlarged ed., Academic Press, New York, 1980.