# A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRALS AND FOURIER-FEYNMAN TRANSFORMS ON FUNCTION SPACE

• Published : 2003.08.01
• 63 12

#### Abstract

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

#### Keywords

generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;Fubinitheorem

#### References

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#### Cited by

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2. A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE vol.50, pp.1, 2013, https://doi.org/10.4134/BKMS.2013.50.1.217
3. Some relationships for the double modified generalized analytic function space Fourier-Feynman transform and its applications vol.290, pp.4, 2017, https://doi.org/10.1002/mana.201500369
4. generalized analytic Fourier–Feynman transform vol.29, pp.9, 2018, https://doi.org/10.1080/10652469.2018.1497024