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Interpolation problems by completely positive maps
Completely positive map quantum operations dilations Hermitian matrices
2011/1/19
Given commuting families of Hermitian matrices {A1, . . . ,Ak} and {B1, . . . ,Bk},conditions for the existence of a completely positive map Φ, such that Φ(Aj) = Bj for j =1, . . . , k, are studied. A...
An 4n-point Interpolation Formula for Certain Polynomials
4n-point Interpolation Formula Certain Polynomials
2010/12/6
By using some techniques of the divided difference operators, we establish an 4n-point interpolation formula. Certain polynomials, such as Jackson’s 8 7 terminating summation formula, are special case...
Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants
Caffarelli-Kohn-Nirenberg inequality Gagliardo-Nirenberg inequality loga-rithmic Hardy inequality logarithmic Sobolev inequality
2010/12/14
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WL...