Difference Spaces And Invariant Linear Forms (lecture Notes In Mathematics)
by Rodney Nillsen /
1994 / English / PDF
7.1 MB Download
Difference spaces arise by taking sums of finite or fractional
differences. Linear forms which vanish identically on such a space
are invariant in a corresponding sense. The difference spaces of L2
(Rn) are Hilbert spaces whose functions are characterized by the
behaviour of their Fourier transforms near, e.g., the origin. One
aim is to establish connections between these spaces and
differential operators, singular integral operators and wavelets.
Another aim is to discuss aspects of these ideas which emphasise
invariant linear forms on locally compact groups. The work
primarily presents new results, but does so from a clear,
accessible and unified viewpoint, which emphasises connections with
related work.
Difference spaces arise by taking sums of finite or fractional
differences. Linear forms which vanish identically on such a space
are invariant in a corresponding sense. The difference spaces of L2
(Rn) are Hilbert spaces whose functions are characterized by the
behaviour of their Fourier transforms near, e.g., the origin. One
aim is to establish connections between these spaces and
differential operators, singular integral operators and wavelets.
Another aim is to discuss aspects of these ideas which emphasise
invariant linear forms on locally compact groups. The work
primarily presents new results, but does so from a clear,
accessible and unified viewpoint, which emphasises connections with
related work.
