Invariant subspaces and rational approximation
نویسندگان
چکیده
منابع مشابه
Pascal's Triangle, Normal Rational Curves, and their Invariant Subspaces
Each normal rational curve Γ in PG(n, F ) admits a group PΓL(Γ) of automorphic collineations. It is well known that for characteristic zero only the empty and the entire subspace are PΓL(Γ)–invariant. In case of characteristic p > 0 there may be further invariant subspaces. For #F ≥ n+ 2, we give a construction of all PΓL(Γ)–invariant subspaces. It turns out that the corresponding lattice is to...
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In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant sub-spaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.
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Abstract: A complete characterization is given of closed shift-invariant subspaces of L2(IR) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating f...
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In this report, a summary of [1] is given. In [1] the authors provide a complete characterization of closed shift-invariant subspaces of L2(R) and the corresponding approximation order. The characterization of principal shift-invariant spaces is given in terms of the Fourier transform of the generator. The approximation order of a general shift-invariant space is the same as a suitably chosen p...
متن کاملAPPROXIMATION FROM SHIFT-INVARIANT SUBSPACES OF L2(Rd)
A complete characterization is given of closed shift-invariant subspaces of L2(Rd) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating function to...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1971
ISSN: 0022-1236
DOI: 10.1016/0022-1236(71)90036-x