✦ LIBER ✦
Bari–Markus property for Riesz projections of 1D periodic Dirac operators
✍ Scribed by P. Djakov; B. Mityagin
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 202 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The Dirac operators
equation image
with L^2^‐potentials
equation image
considered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions (bc), have discrete spectra, and the Riesz projections
equation image
are well‐defined for |n | ≥ N if N is sufficiently large. It is proved that
equation image
where P^0^ ~n~, n ∈ ℤ, are the Riesz projections of the free operator.
Then, by the Bari–Markus criterion, the spectral Riesz decompositions
equation image
converge unconditionally in L^2^ (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)