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A FUBINI THEOREM FOR INTEGRAL TRANSFORMS AND CONVOLUTION PRODUCTS
Preview AbstractIn this paper we establish Fubini theorems for integral transforms and convolution products for functionals on function space.
VANISHING THEOREM OF THE HODGE–KODAIRA OPERATOR FOR DIFFERENTIAL FORMS ON A CONVEX DOMAIN OF THE WIENER SPACE
Preview AbstractWe discuss the vanishing theorem on a convex domain of the Wiener space. We show that there is no harmonic form satisfying the absolute boundary condition. Our method relies on an expression of the bilinear form associated with the Hodge–Kodaira operator.
Domains of elliptic operators on sets in Wiener space
Preview AbstractLet X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron–Martin space is denoted by H. Consider two sufficiently regular convex functions U:X→ℝ and G:X→ℝ. We let ν=e−Uμ and Ω=G−1(−∞,0]. In this paper, we study the domain of the self-adjoint operator associated with the quadratic form
(ψ,φ)↦∫Ω〈∇Hψ,∇Hφ〉Hdνψ,φ∈W1,2(Ω,ν),(0.1)and we give sharp embedding results for it. In particular, we obtain a characterization of the domain of the Ornstein–Uhlenbeck operator in Hilbert space with Ω=X and on half-spaces, namely if U≡0 and G is an affine function, then the domain of the operator defined via (0.1) is the space{u∈W2,2(Ω,μ)|〈∇Hu(x),∇HG(x)〉H=0 for ρ-a.e. x∈G−1(0)},where ρ is the Feyel–de La Pradelle Hausdorff–Gauss surface measure.The average errors for linear combinations of Bernstein–Kantorovich operators on the Wiener space
Preview AbstractIn this paper, we discuss the average errors of function approximation by linear combinations of Bernstein–Kantorovich operators. The strongly asymptotic orders for the average errors of these operators sequence are determined on the Wiener space.