Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

Streszczenie

Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vector-valued functions via tensor product theory. In this paper we study weighted spaces $\mathcal {EV}(\Omega )$ of smooth functions on an open subset $\Omega \subset \mathbb R ^{d}$ whose topology is given by a family $\mathcal {V}$ of weights. We derive sufficient conditions on the weights to make $\mathcal {EV}(\Omega )$ a nuclear space.