Djakov, Plamen Borissov and Mityagin, Boris Samuel (2010) BariMarkus property for Riesz projections of 1D periodic Dirac operators. Mathematische Nachrichten, 283 (3). pp. 443462. ISSN 0025584X
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Official URL: http://dx.doi.org/10.1002/mana.200910003
Abstract
The Dirac operators
Ly = i ((1)(0) (0)(1))dy/dx + v(x)y, y = ((y1)(y2)), x is an element of[0, pi],
with L2potentials
v(x) = ((0)(Q(x)) (P(x))(0)), P, Q is an element of L2([0, pi]), considered on [0, pi] with periodic, antiperiodic or Dinchlet boundary conditions (bc), have discrete spectra, and the Riesz projections,
SN = 1/2 pi iota integral(vertical bar z vertical bar=N  1/2) (z  Lbc)(1) dz. p(n) = 1/2 pi iota integral(vertical bar zn vertical bar=1/2) (z  Lbc)(1) dz
are welldefined for vertical bar n vertical bar >= N if N is sufficiently large. It is proved that
Sigma(vertical bar n vertical bar>N) parallel to Pn  Pn(0)parallel to(2) < infinity, where Pn(0), n is an element of Z,
are the Riesz projections of the free operator.
Then, by the Ban Markus criterion, the spectral Riesz decompositions
f = SN + Sigma(vertical bar n vertical bar>N) P(n)f, for all f is an element of L2
converge unconditionally in L2. (C) 2010 WILEYVCH Verlag GmbH & Co KGaA, Weinhom
Item Type:  Article 

Uncontrolled Keywords:  1D periodic Dirac operator, Riesz projections, spectral decomposition 
Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis 
Divisions:  Faculty of Engineering and Natural Sciences 
Depositing User:  Plamen Borissov Djakov 
Date Deposited:  12 Mar 2010 11:11 
Last Modified:  26 Apr 2022 08:36 
URI:  https://research.sabanciuniv.edu/id/eprint/13824 
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BariMarkus property for Riesz projections of 1D periodic Dirac operators. (deposited 04 Nov 2009 21:30)
 BariMarkus property for Riesz projections of 1D periodic Dirac operators. (deposited 12 Mar 2010 11:11) [Currently Displayed]