Characterization of surjective convolution operators on Sato's hyperfunctions

• Autorzy: Michael Langenbruch
• Języki publikacji: EN

Abstrakty

EN

Let $μ ∈ 𝓐 (ℝ^{d})'$ be an analytic functional and let $T_μ$ be the corresponding convolution operator on Sato's space $𝓑 (ℝ^{d})$ of hyperfunctions. We show that $T_μ$ is surjective iff $T_μ$ admits an elementary solution in $𝓑 (ℝ^{d})$ iff the Fourier transform μ̂ satisfies Kawai's slowly decreasing condition (S). We also show that there are $0 ≠ μ ∈ 𝓐 (ℝ^{d})'$ such that $T_μ$ is not surjective on $𝓑 (ℝ^{d})$.

Kategorie tematyczne

• 46N20: Applications to differential and integral equations
• 44A35: Convolution
• 46F15: Hyperfunctions, analytic functionals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 88
• Numer: 1
• Strony: 185-193

Daty

wydano

2010

Twórcy

autor

Michael Langenbruch

• Department of Mathematics, University of Oldenburg, 26111 Oldenburg, Germany

Identyfikatory

DOI

10.4064/bc88-0-15