Perturbations of Orthogonal Polynomials with Periodic Recursion Coefficients

@inproceedings{Damanik2007PerturbationsOO,
  title={Perturbations of Orthogonal Polynomials with Periodic Recursion Coefficients},
  author={David Damanik and Rowan Killip and Barry Simon},
  year={2007}
}
We extend the results of Denisov–Rakhmanov, Szegő–Shohat– Nevai, and Killip–Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 89 references

Perturbations of one-dimensional Schrödinger operators preserving the absolutely continuous spectrum

R. Killip
Int. Math. Res. Not • 2002
View 11 Excerpts
Highly Influenced

The scattering problem for a discrete Sturm–Liouville

A. I. Aptekarev, E. M. Nikishin
operator, Math USSR Sb • 1984
View 4 Excerpts
Highly Influenced

Orthogonal polynomials from the viewpoint of scattering theory

K. M. Case
J. Math. Phys • 1974
View 6 Excerpts
Highly Influenced

Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory, AMS Colloquium

B. Simon
2005
View 8 Excerpts
Highly Influenced

Zlatoš, Sum rules and the Szegő condition for orthogonal polynomials on the real line

A. B. Simon
Comm. Math. Phys • 2003
View 5 Excerpts
Highly Influenced

Năıman, On the spectral theory of non-symmetric periodic Jacobi matrices, Zap

P B.
Meh.- Mat. Fak. Har’kov. Gos. Univ. i Har’kov. Mat. Obšč • 1964
View 12 Excerpts
Highly Influenced

Năıman, On the theory of periodic and limit-periodic Jacobian matrices

P B.
Soviet Math. Dokl • 1962
View 10 Excerpts
Highly Influenced

Chulaevsky, An inverse spectral problem for limit-periodic Schrödinger operators

V A.
Functional Anal. Appl • 1984
View 4 Excerpts
Highly Influenced

Spectral theory via sum rules, Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday (F

R. Killip
Gesztesy et al., eds.), • 2007

Similar Papers

Loading similar papers…