Translation and modulation invariant Hilbert spaces
Keyword(s):
AbstractLet $$\mathcal H$$ H be a Hilbert space of distributions on $$\mathbf{R}^{d}$$ R d which contains at least one non-zero element of the Feichtinger algebra $$S_0$$ S 0 and is continuously embedded in $$\mathscr {D}'$$ D ′ . If $$\mathcal H$$ H is translation and modulation invariant, also in the sense of its norm, then we prove that $$\mathcal H= L^2$$ H = L 2 , with the same norm apart from a multiplicative constant.
Keyword(s):
2005 ◽
Vol 71
(1)
◽
pp. 107-111
Keyword(s):
Keyword(s):
2008 ◽
Vol 60
(5)
◽
pp. 1001-1009
◽
Keyword(s):
2012 ◽
Vol 09
(02)
◽
pp. 1260005
◽
1984 ◽
Vol 25
(1)
◽
pp. 99-101
◽
Keyword(s):
1999 ◽
Vol 22
(1)
◽
pp. 97-108
◽
Keyword(s):