Research Papers

Analytic representation of the duals of weighted function spaces

I. A. Filip'ev

JSC “VNII “Gradient”

Abstract: A class of locally convex spaces is considered, which contains weighted spaces of infinitely differentiable, holomorphic, or ultradifferentiable functions and some other spaces. For spaces from this class, an algebraic description of the conjugate space is provided. As applications of this result, analogs of the Paley–Wiener–Schwartz theorem for spaces of ultradifferentiated functions and other classes of function spaces are obtained.

Keywords: Fourier–Laplace transformation of functionals, continuation of holomorphic functions, dual space, ultradifferentiable functions, weighted functional spaces.

Received: 14.02.2025