INTEGRATION STRUCTURES FOR THE OPERATOR-VALUED FEYNMAN INTEGRAL

  • Published : 2001.03.01

Abstract

The analytic in mass operator-valued Feynman integral is related to integration with respect to unbounded set functions formed from the semigroup obtained by analytic continuation of the heat semigroup and the spectral measure of multiplication by characteristics functions.

Keywords

References

  1. Acta Appl.Math v.42 The analytic operator-valued Feynman integral via addivive functionals of Brownian motion S.Albecerio;G.W.Johnson;Z.M.Ma
  2. J.of Math.and Physics v.39 A family of integrals serving to connect Wiener and Feynman integrals R.H.Cameron
  3. J.Math.and Mech v.18 An operator-valued function space integral and a related equation R.H.Cameron;D.A.Storvick
  4. Uspekhi Matem.Nauk v.17 Functional integrals connected with operator evloution equations Yu.L.Daletskii
  5. Russ,Math.Surveys v.17 Yu.L.Daletskii
  6. Princeton U.P. Harmonic Analysis in Phase Space G.B.Folland
  7. Publ.Res.Inst.Math.Sci. v.21 Remarks on the Feynman representation B.Jefferies
  8. Kluwer Acad. Publ.Dordrecht Remarks on the Feynman representation B.Jefferies
  9. J.Math v.38 Pettis integrals and singular integral operators,Ⅲ B.Jefferies;S,Okada
  10. J.Austral.Math.Soc.Ser.A v.56 Integraltion with respect to vector valued Radon polumeasures B,Jefferies;W,Ricker
  11. Pacific J.Math v.83 Scale-invariant measurability in Wiener space G,W,Johnson;D,L,Skoung
  12. Oxford Mathematical Monograph The Feynman Integral and Feynman's Operationa Caculus G.W.Hohnson;M.L.Lapidus
  13. Perturbation Theory for Linear Operatiors,2nd Ed T.Kato
  14. Contemporary Mathematics v.2 Applications of Vector Measures I.Kluvanek
  15. Arch.Rat.Mech. & Anal v.81 Operator valued measures and perturbations of semi-groups I.Kluvanek
  16. Studia Math. v.86 Integraltion and the Feynman-Kac formula I,Kluvanek
  17. Proc. Centre for Mathematical Analysis v.18 Integraltion structures I,Kluvanek
  18. Proc. Centre for Mathematical Analysis v.24 Four remarks concerning the Feynman integral I,Kluvanek
  19. J.Math.Phys v.5 Feynman integrals and the Schrodinger equation E,Nelson
  20. Methods of Modern Mathematical Physics Ⅱ M.Reed;B.Simon
  21. Acta Appl.Math v.43 Path integrals on finite sets E,Thomas
  22. Proc. Sympos. Appl. Math;Amer.Math.Soc.Providence,RI v.52 Finite path integrals, Proceedings of the Norbert Wiener Centenary Congress,1994(East Lansing,MI,1994) E,Thomas