2,379 research outputs found
Approximation of Entropy Numbers
The purpose of this article is to develop a technique to estimate certain
bounds for entropy numbers of diagonal operator on spaces of p-summable
sequences for finite p greater than 1. The approximation method we develop in
this direction works for a very general class of operators between Banach
spaces, in particular reflexive spaces. As a consequence of this technique we
also obtain that the entropy number of a bounded linear operator T between two
separable Hilbert spaces is equal to the entropy number of the adjoint of T.
This gives a complete answer to the question posed by B. Carl [4] in the
setting of separable Hilbert spaces.Comment: 10 page
Sato-Tate groups of some weight 3 motives
We establish the group-theoretic classification of Sato-Tate groups of
self-dual motives of weight 3 with rational coefficients and Hodge numbers
h^{3,0} = h^{2,1} = h^{1,2} = h^{0,3} = 1. We then describe families of motives
that realize some of these Sato-Tate groups, and provide numerical evidence
supporting equidistribution. One of these families arises in the middle
cohomology of certain Calabi-Yau threefolds appearing in the Dwork quintic
pencil; for motives in this family, our evidence suggests that the Sato-Tate
group is always equal to the full unitary symplectic group USp(4).Comment: Minor edits to correct typos and address LMFDB modular form label
change
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