A sequential analytic Feynman integral of functionals in L₂(C₀[0, T])

Abstract

In this paper, we define a sequential analytic Feynman integral of functionals on Wiener space. We then give the existence of the sequential analytic Feynman integral of functionals in L ₂(C ₀[0, T]). The expansion of functionals in L ₂(C ₀[0, T]) in terms of Fourier–Hermite functionals plays a key role in the study.

Keywords:

• a sequential Feynman integral
• Fourier–Hermite functional
• complete orthonormal set
• Wiener space

AMS Subject Classification :

• Primary: 60J65
• 28C20