Abstract
AbstractIn this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $${\mathcal S}({\mathbb R})$$
S
(
R
)
of rapidly decreasing functions, i.e., operators of the form $$M_h: {\mathcal S}({\mathbb R})\rightarrow {\mathcal S}({\mathbb R})$$
M
h
:
S
(
R
)
→
S
(
R
)
, $$f \mapsto h f $$
f
↦
h
f
, and $$C_T:{\mathcal S}({\mathbb R})\rightarrow {\mathcal S}({\mathbb R})$$
C
T
:
S
(
R
)
→
S
(
R
)
, $$f\mapsto T\star f$$
f
↦
T
⋆
f
. Precisely, we determine their spectra and characterize when those operators are power bounded and mean ergodic.
Publisher
Springer Science and Business Media LLC
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