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The structure of quasiasymptotics of Schwartz distributions

Jasson Vindas (2010)

Banach Center Publications

In this article complete characterizations of the quasiasymptotic behavior of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to quasiasymptotics of degree -1. It is shown how the structural theorem can be used to study Cesàro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed. A condition for test functions in bigger spaces...

The Taylor transformation of analytic functionals with non-bounded carrier

Grzegorz Łysik (1994)

Studia Mathematica

Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.

The ℒ ν ( ρ ) -transformation on McBride’s spaces of generalized functions

Domingo Israel Cruz-Báez, Josemar Rodríguez (1998)

Commentationes Mathematicae Universitatis Carolinae

An integral transform denoted by ℒ ν ( ρ ) that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.

Topological classification of strong duals to nuclear (LF)-spaces

Taras Banakh (2000)

Studia Mathematica

We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: ℝ ω , ℝ ∞ , Q × ℝ ∞ , ℝ ω × ℝ ∞ , or ( ℝ ∞ ) ω , where ℝ ∞ = l i m ℝ n and Q = [ - 1 , 1 ] ω . In particular, the Schwartz space D’ of distributions is homeomorphic to ( ℝ ∞ ) ω . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to ℝ ∞ or to Q × ℝ ∞ . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either...

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