Samenvatting
It is shown that there is a tradeoff between the smoothness and decay properties of the dual functions, occurring in the lattice expansion problem. More precisely, it is shown that if g and g¯ are dual, then (1) at least one of H1/2 g and H1/2 g¯ is n in L2(R), and (2) at least one of Hg and g ¯ is not in L2(R). Here, H is the operator -1/(4p2)d2/(dt2 )+t2. The first result is a generalization of a theorem first stated by R.C. Balian (1987). The second result is new and relies heavily on the fact that, when G¿W2,2(S) with S=[-1/2, 1/2]×[-1/2, 1/2] and G(0), than 1/G¿L 2(S)
Originele taal-2 | Engels |
---|---|
Pagina's (van-tot) | 3-6 |
Aantal pagina's | 4 |
Tijdschrift | IEEE Transactions on Information Theory |
Volume | 39 |
Nummer van het tijdschrift | 1 |
DOI's | |
Status | Gepubliceerd - 1993 |