The inverse problem for the Hill operator, a direct approach

Inventiones Mathematicae

Volumn 129, Issue 3, 1997, Pages 567-593

  Kargaev, Pavel ^a   Korotyaev, Evgeni ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b SAINT PETERSBURG ELECTROTECHNICAL UNIVERSITY LETI   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031493397     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050173     Document Type: Article

References (16)

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2. [Fr] Fryntov, A.: An extremal problem of potential theory. Soviet Math. Dokl. 37, 754-755 (1988)
3. Garnett, J., Trubowitz, E.: Gaps and bands of one dimensional periodic Schrödinger operators. Comment. Math. Helv. 59, 258-312 (1984)
4. Garnett, J., Trubowitz, E.: Gaps and bands of one dimensional periodic Schrödinger operators II. Comment. Math. Helv. 62, 18-37 (1987)
5. [IM] Its, A., Matveev, V.: Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteveg de Vries equation. Theoret. Math. Phys. 23, 343-355 (1975)
6. [KK] Kargaev, P., Korotyaev, E.: Effective masses and conformal mappings. Commun. Math. Phys. 169, 597-625 (1995)
7. Korotyaev, E.: Propagation of waves in one-dimensional periodic media. (To be published in Asymptotic. Anal.)
8. Korotyaev, E.: Some equalities for the Hill operator. (To be published)
9. Korotyaev, E.: The estimate of periodic potentials in terms of effective masses. Commun. Math. Phys. 183, 383-400 (1997)
10. Korotyaev, E.: Uniform estimates for the Hill operator. (To be published in Dokl. Akad. Nauk.) (in Russian)
11. Levin, B.: Majorants in classes of subharmonic functions. 1-3. Theory of functions, functional analysis and their applications. 51, 3-17 (1989); 52, 3-33 (1989) (in Russian)
12. Levin, B.: Majorants in classes of subharmonic functions. 1-3. Theory of functions, functional analysis and their applications. 51, 3-17 (1989); 52, 3-33 (1989) (in Russian)
13. Marchenko, V.: Sturm-Liouville operator and applications. Basel: Birkhäuser 1986
14. [MO] Marchenko, V., Ostrovski, I.: A characterization of the spectrum of the Hill operator. Math. USSR Sbornik 26, 493-554 (1975)
15. [PT] Pöschel, P., Trubowitz, E.: Inverse Spectral Theory. Boston: Academic Press 1987
16. [T] Titchmarsh, E.: Eigenfunction expansions associated with second-order differential equations 2, Oxford: Clarendon Press 1958