References
N. I. Akhiezer,Orthogonal polynomials on a system of intervals and its continual analogues, Proc. of the 4th All-Union mathem. Congress, vol. 2, 1964, pp. 623–628 (Russian)
N. I. Akhiezer,On an undetermined equation of Chebyshev type in problems of construction of orthogonal systems. Math. physics and functional analysis (Proceed. Inst. Low. Temp. Physics, Kharkov)2 (1971), 3–14 (Russian)
N. i. Akhiezer,Some inverse problems of spectral theory connected with hyperelliptic integrals, (Russian), Theory of linear operators in Hilbert space (by N. I. Akhiezer and I. M. Glazman), vol. 2, Kharkov, 1978, pp. 242–283.
N. I. Akhiezer andB. Ya. Levin,Generalization of S. N. Bernstein's inequality for derivatives of entire functions, (Russian), Issledovaniya po sovremennym problemam teorii funktsii kompleksnogo peremennogo (A. I. Markushevich, ed.), Nauka, Moscow, 1961, pp. 111–165; French transl. in Fonctions d'une variable complexe. Problemes contemporains, Gauthier-Villars, Paris, 1962.
N. I. Akhiezer andA. M. Rybalko,Continual analogs of polynomials orthogonal on a circle, Ukrainian Math. J.20 (1968), 1–21.
E. D. Belokolos, A. I. Bobenko, V. Z. Enol'skii, A. R. Its andV. B. Matveev,Algebro-Geometric Approach to Nonlinear Integrable Systems, Springer Series in Nonlinear Dynamics, Springer-Verlag, Berlin, 1994.
L. Carleson,On H ∝ in multiply connected domains, Conference on harmonic analysis in honor Antoni Zygmund (W Beckner, et al. eds.), vol. II, Wadsworth, 1983, pp. 349–372.
R. Carmona andJ. Lacroix,Spectral theory of Random Schrödinger Operators, Birkhauser, Boston, 1990.
W. Craig,Trace formula for Schrödinger operator on the line, Commun. Math. Phys.126 (1989), 379–408.
B. A. Dubrovin, V. B. Matveev andS. P. Novikov,Nonlinear equations of Korteweg-de Vries type, finite zone linear operators and Abelian varieties. Russian Math. Surveys31 (1976), 59–146.
I. E. Egorova,On one class of almost-periodic solutions of KdV with nowhere dense spectrum, Russian Math. Dokl.45 (1992), 290–293.
I. E. Egorova,Almost periodicity of solutions of the KdV equation with Cantor spectrum, (Russian), Dopovidi Ukrain, Akad. Nauk (1993), no. 7, 26–29.
J. Garnett andE. Trubowitz,Gaps and bands of one dimensional periodic Shrödinger operators I, Comment. Math. Helvetici59 (1984), 258–312; II, ibidJ. Garnett andE. Trubowitz,Gaps and bands of one dimensional periodic Shrödinger operators, I, Comment. Math. Helvetici62 (1987), 18–37.
P. Jones andD. Marshall,Critical points of Green's function, harmonic measure, and the corona problem, Arkiv för Mathematik23 (1985), 281–314.
M. G. Krein andA. A. Nudelman,The Markov moment problem and extremal problems, Amer. Math. Soc., Providence, RI, 1977.
N. S. Landkof,Foundations of modern potential theory, Springer, Berlin, 1972.
B. Ya. Levin,Majorants in classes of subharmonic functions, I, Function Theory, Functional Analysis and their Applications (Kharkov)51 (1989), 3–17; II, III, ibidB. Ya. Levin,Majorants in classes of subharmonic functions, II, III, Function Theory, Functional Analysis and their Applications (Kharkov)52 (1989), 3–33 (Russian); English transl. in Jour. Soviet Math.52 (1990).
B. M. Levitan,Inverse Sturm-Liouville problems, (Russian), Nauka, Moscow, 1984.
B. M. Levitan,On the closure of the set of finite-band potentials, Math. USSR Sbornik51 (1985), 67–89.
V. A. Marchenko,Sturm-Liouville Operators and Applications, (Russian), Kiev, 1977.
V. A. Marchenko andI. V. Ostrovskii,A characterization of the spectrum of Hill's operator, Math. USSR Sbornik97 (1975), 493–554.
V. A. Marchenko andI. V. Ostrovskii,Approximation of periodic by finite-zone potentials, Selecta Mathematica Sovetica6 (1987), 103–136.
H. P. McKean andP. van Moerbeke,The Spectrum of Hill's Equation, Invent. Math.30 (1975), 217–274.
H. P. McKean andE. Trubowitz,Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points, Commun. Pure Appl. Math.29 (1976), 143–226.
H. P. McKean andE. Trubowitz,Hill's surfaces and their theta-functions, Bull. Amer. Math. Soc.84 (1977), 1042–1085.
J. Moser,Integrable Hamiltonian Systems and Spectral Theory, Accademia Nazionale dei Lincei Scuola Normale Superiore, Pisa, 1984.
L. A. Pastur andV. A. Tkachenko,Spectral theory of a class of one-dimensional Schrödinger operators with limit-periodic potentials, Trans. Moscow Math. Soc.51 (1989), 115–118.
L. A. Pastur andA. Figotin,Spectra of Random and Almost-Periodic Operators, Springer-Verlag, Berlin, 1992.
M. Sodin andP. Yuditskii,Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions, to appear, Journal of Geometric Analysis.
E. Titchmarsh,Eigenfunction expansions associated with second-order differential equations, Clarendon, Oxford, 1946.
H. Widom,The maximum principle for multiple valued analytic functions, Acta Math.126 (1971), 63–81.
Author information
Authors and Affiliations
Additional information
To the memory of B. Ya. Levin (1906–1993) who was a teacher of our teachers and who gave us so much
This work was partially supported by ISF Grant no. U2Z000.
Rights and permissions
About this article
Cite this article
Sodin, M., Yuditskii, P. Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum. Commentarii Mathematici Helvetici 70, 639–658 (1995). https://doi.org/10.1007/BF02566026
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02566026