Displaying similar documents to “Families of reduced zero-dimensional schemes.”

Remarks on the Hilbert transform and on some families of multiplier operators related to it.

Enrico Laeng (2007)

Collectanea Mathematica

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We give an overview of the behavior of the classical Hilbert Transform H seen as an operator on L(R) and on weak-L(R), then we consider other operators related to H. In particular, we discuss various versions of Discrete Hilbert Transform and Fourier multipliers periodized in frequency, giving some partial results and stating some conjectures about their sharp bounds L(R) → L(R), for 1 < p < ∞.

On the algebraic structure of the unitary group.

Éric Ricard, Christian Rosendal (2007)

Collectanea Mathematica

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We consider the unitary group U of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever U acts by isometries on a metric space, every orbit is bounded. Equivalently, U is not the union of a countable chain of proper subgroups, and whenever E ⊆ U generates U, it does so by words of a fixed finite length.