Regularity and the Cesàro-Nevai class

Journal of Approximation Theory

Volumn 156, Issue 2, 2009, Pages 142-153

  Simon, Barry ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Orthogonal polynomial; Regular measure

Indexed keywords

EID: 59349099108     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2008.04.016     Document Type: Article

References (27)

1. Chihara T.S. An Introduction to Orthogonal Polynomials. Mathematics and Its Applications vol. 13 (1978), Gordon and Breach, New York, London, Paris. MR0481884
2. J.S. Christiansen, B. Simon, M. Zinchenko, Finite gap Jacobi matrices, I. The isospectral torus (preprint)
3. Damanik D., Hundertmark D., Killip R., and Simon B. Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Comm. Math. Phys. 238 (2003) 545-562. MR1993385
4. Damanik D., Hundertmark D., and Simon B. Bound states and the Szego{double acute} condition for Jacobi matrices and Schrödinger operators. J. Funct. Anal. 205 (2003) 357-379. MR2017691
5. Damanik D., Killip R., and Simon B. Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Int. Math. Res. Not. 22 (2004) 1087-1097. MR2041649
6. D. Damanik, R. Killip, B. Simon, Perturbations of orthogonal polynomials with periodic recursion coefficients, preprint
7. Damanik D., Pushnitski A., and Simon B. The analytic theory of matrix orthogonal polynomials. Surv. Approx. Theory 4 (2008) 1-85
8. Freud G. Orthogonal Polynomials (1971), Pergamon Press, Oxford, New York
9. Geronimus Ya.L. Orthogonal Polynomials: Estimates, Asymptotic Formulas, and Series of Polynomials Orthogonal on the Unit Circle and on an Interval (1961), Consultants Bureau, New York. MR0133643
10. Golinskii L., and Khrushchev S. Cesàro asymptotics for orthogonal polynomials on the unit circle and classes of measures. J. Approx. Theory 115 (2002) 187-237. MR1901215
11. Killip R., and Simon B. Sum rules for Jacobi matrices and their applications to spectral theory. Ann. of Math. 158 (2003) 253-321. MR1999923
12. Landkof N.S. Foundations of Modern Potential Theory (1972), Springer-Verlag, Berlin, New York. MR0350027
13. Last Y., and Simon B. The essential spectrum of Schrödinger, Jacobi, and CMV operators. J. Anal. Math. 98 (2006) 183-220. MR2254485
14. Máté A., Nevai P., and Totik V. Extensions of Szego{double acute}'s theory of orthogonal polynomials, II. Constr. Approx. 3 (1987) 51-72. MR0892168
15. Nevai P. Orthogonal polynomials. Mem. Amer. Math. Soc. 18 213 (1979) 185. MR0519926
16. Ransford T. Potential Theory in the Complex Plane. London Mathematical Society Student Texts vol. 28 (1995), Cambridge University Press, Cambridge. MR1334766
17. C. Remling, The absolutely continuous spectrum of Jacobi matrices, preprint
18. Simon B. Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory. AMS Colloquium Publications vol. 54.1 (2005), American Mathematical Society, Providence, RI. MR2105088
19. Simon B. Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory. AMS Colloquium Publications vol. 54.2 (2005), American Mathematical Society, Providence, RI. MR2105089
20. Simon B. Trace Ideals and Their Applications. second edition. Mathematical Surveys and Monographs vol. 120 (2005), American Mathematical Society, Providence, RI. MR2105089
21. Simon B. CMV matrices: Five years after. J. Comput. Appl. Math. 208 (2007) 120-154. MR2347741
22. Simon B. Equilibrium measures and capacities in spectral theory. Inverse Problems and Imaging 1 (2007) 713-772. MR2350223
23. 2 Perturbations of Orthogonal Polynomials, Princeton University Press (in preparation)
24. Sodin M., and Yuditskii P. Almost periodic Jacobi matrices with homogeneous spectrum, infinite-dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions. J. Geom. Anal. 7 (1997) 387-435. MR1674798
25. Stahl H., and Totik V. General Orthogonal Polynomials. Encyclopedia of Mathematics and its Applications vol. 43 (1992), Cambridge University Press, Cambridge. MR1163828
26. Szego{double acute} G. Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. vol. 23 (1939), American Mathematical Society, Providence, R.I third edition, 1967. MR0000077
27. Ullman J.L. On the regular behaviour of orthogonal polynomials. Proc. London Math. Soc. 24 3 (1972) 119-148. MR0291718