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Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Tuesday, July 20, 19:05 ~ 19:35 UTC-3

Nonnegativity and spanning structure

Alex Powell

Vanderbilt University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We investigate nonnegativity as an obstruction to various types of spanning structure in Lp spaces. For example, if a system of functions is pointwise nonnegative, then it cannot be a frame or Riesz basis for L2, or an unconditional quasibasis for Lp. On the other hand, there exist pointwise nonnegative Markushevich bases and conditional quasibases in Lp, and in recent work we show that L2 admits a nonnegative Schauder basis.

Joint work with Dan Freeman (Saint Louis University, USA), Mitchell Taylor (University of California, Berkeley, USA) and Anneliese Spaeth (Huntingdon College, USA).

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