On generalized local time for the process of brownian motion - Вакип, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We prove that the functionals \(δ _Γ (B_t ) and \frac{{\partial ^k }}{{\partial x_1^k ...\partial x_d^{k_d } }}δ _Γ (B_t ), k_1 + ... + k_d = k > 1,\) of a d-dimensional Brownian process are Hida distributions, i.e., generalized Wiener functionals. Here, δΓ(·) is a generalization of the δ-function constructed on a bounded closed smooth surface Γ⊂R d , k≥1 and acting on finite continuous functions φ(·) in R d according to the rule \((δ _Γ ,φ ) : = \int\limits_Γ {φ (x} )λ (dx),\) where ι(·) is a surface measure on Γ.