Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ANALYTIC OPERATOR-VALUED GENERALIZED FEYNMAN INTEGRALS ON FUNCTION SPACE

  • Received : 2009.09.13
  • Accepted : 2010.01.18
  • Published : 2010.03.30
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Abstract

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

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References

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