Develops theory of Berger-type charges for weighted shifts, proving k-hyponormality implies positivity of largest k+1 atom densities in signed atomic measures and charge representations for hyperexpansive shifts.
Bhatia, Infinitely divisible matrices, Amer
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A two-parameter family of geometrically regular weighted shifts is introduced and shown to realize moment infinite divisibility, subnormality, k-hyponormality, or complete hyperexpansiveness in different sectors of the (N,D) parameter square.
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Signed representing measures (Berger-type charges) in subnormality and related properties of weighted shifts
Develops theory of Berger-type charges for weighted shifts, proving k-hyponormality implies positivity of largest k+1 atom densities in signed atomic measures and charge representations for hyperexpansive shifts.
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Geometrically regular weighted shifts
A two-parameter family of geometrically regular weighted shifts is introduced and shown to realize moment infinite divisibility, subnormality, k-hyponormality, or complete hyperexpansiveness in different sectors of the (N,D) parameter square.