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Funktsional. Anal. i Prilozhen., 1978, Volume 12, Issue 3, Pages 20–31 (Mi faa2002)  

This article is cited in 57 scientific papers (total in 57 papers)

Commutative rings of ordinary linear differential operators

I. M. Krichever

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English version:
Functional Analysis and Its Applications, 1978, 12:3, 175–185

Bibliographic databases:

UDC: 517.43
Received: 15.02.1977

Citation: I. M. Krichever, “Commutative rings of ordinary linear differential operators”, Funktsional. Anal. i Prilozhen., 12:3 (1978), 20–31; Funct. Anal. Appl., 12:3 (1978), 175–185

Citation in format AMSBIB
\by I.~M.~Krichever
\paper Commutative rings of ordinary linear differential operators
\jour Funktsional. Anal. i Prilozhen.
\yr 1978
\vol 12
\issue 3
\pages 20--31
\jour Funct. Anal. Appl.
\yr 1978
\vol 12
\issue 3
\pages 175--185

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    This publication is cited in the following articles:
    1. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over Riemann surfaces and the Kadomtsev–Petviashvili equation. I”, Funct. Anal. Appl., 12:4 (1978), 276–286  mathnet  crossref  mathscinet  zmath
    2. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over algebraic curves and non-linear equations”, Russian Math. Surveys, 35:6 (1980), 53–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Sokolov, A. B. Shabat, “$(L,A)$-Pairs and a Ricatti type substitution”, Funct. Anal. Appl., 14:2 (1980), 148–150  mathnet  crossref  mathscinet  zmath
    4. I. M. Krichever, “Self-similar solutions of equations of Korteweg -de Vries type”, Funct. Anal. Appl., 14:3 (1980), 234–236  mathnet  crossref  mathscinet  zmath  isi
    5. I. M. Krichever, “Baxter's equations and algebraic geometry”, Funct. Anal. Appl., 15:2 (1981), 92–103  mathnet  crossref  mathscinet  zmath  isi
    6. O. I. Mokhov, “Commuting ordinary differential operators of rank 3 corresponding to an elliptic curve”, Russian Math. Surveys, 37:4 (1982), 129–130  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. P. G. Grinevich, “Rational solutions for the equation of commutation of differential operators”, Funct. Anal. Appl., 16:1 (1982), 15–19  mathnet  crossref  mathscinet  zmath  isi
    8. S. I. Svinolupov, “Analogs of the Burgers equation of arbitrary order”, Theoret. and Math. Phys., 65:2 (1985), 1177–1180  mathnet  crossref  mathscinet  zmath  isi
    9. P. G. Grinevich, “Vector rank of commuting matrix differential operators. Proof of S. P. Novikov's criterion”, Math. USSR-Izv., 28:3 (1987), 445–465  mathnet  crossref  mathscinet  zmath
    10. F. Kh. Mukminov, V. V. Sokolov, “Integrable evolution equations with constraints”, Math. USSR-Sb., 61:2 (1988), 389–410  mathnet  crossref  mathscinet  zmath
    11. V. A. Zolotarev, “Model representations of commutative systems of linear operators”, Funct. Anal. Appl., 22:1 (1988), 55–57  mathnet  crossref  mathscinet  zmath  isi
    12. O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655  mathnet  crossref  mathscinet  zmath
    13. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. S. P. Novikov, “Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory”, Funct. Anal. Appl., 24:4 (1990), 296–306  mathnet  crossref  mathscinet  zmath  isi
    15. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. V. I. Dragovich, “Solutions of the Yang equation with rational irreducible spectral curves”, Russian Acad. Sci. Izv. Math., 42:1 (1994), 51–65  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. D. P. Novikov, “Algebraic-geometric solutions of the Krichever–Novikov equation”, Theoret. and Math. Phys., 121:3 (1999), 1567–1573  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. I. M. Krichever, S. P. Novikov, “Holomorphic bundles and scalar difference operators: one-point constructions”, Russian Math. Surveys, 55:1 (2000), 180–181  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    20. I. M. Krichever, S. P. Novikov, “Holomorphic bundles and commuting difference operators. Two-point constructions”, Russian Math. Surveys, 55:3 (2000), 586–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. I. M. Krichever, “Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations”, Mosc. Math. J., 2:4 (2002), 717–752  mathnet  crossref  mathscinet  zmath  elib
    22. I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. A. E. Mironov, “Discrete analogues of Dixmier operators”, Sb. Math., 198:10 (2007), 1433–1442  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    24. O. K. Sheinman, “Lax Operator Algebras and Integrable Hierarchies”, Proc. Steklov Inst. Math., 263 (2008), 204–213  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    25. A. E. Mironov, “O kommutiruyuschikh differentsialnykh operatorakh ranga $2$”, Sib. elektron. matem. izv., 6 (2009), 533–536  mathnet  mathscinet  elib
    26. O. K. Sheinman, “Lax operator algebras and Hamiltonian integrable hierarchies”, Russian Math. Surveys, 66:1 (2011), 145–171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    27. A. B. Zheglov, A. E. Mironov, “Moduli Beikera – Akhiezera, puchki Krichevera i kommutativnye koltsa differentsialnykh operatorov v chastnykh proizvodnykh”, Dalnevost. matem. zhurn., 12:1 (2012), 20–34  mathnet
    28. Dafeng Zuo, “Commuting differential operators of rank 3 associated to a curve of genus 2”, SIGMA, 8 (2012), 044, 11 pp.  mathnet  crossref  mathscinet
    29. V. E. Adler, V. G. Marikhin, A. B. Shabat, “Quantum tops as examples of commuting differential operators”, Theoret. and Math. Phys., 172:3 (2012), 1187–1205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    30. Brezhnev Yu.V., “Spectral/Quadrature Duality: Picard-Vessiot Theory and Finite-Gap Potentials”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 1–31  crossref  isi
    31. V. N. Davletshina, “O samosopryazhennykh kommutiruyuschikh differentsialnykh operatorakh ranga dva”, Sib. elektron. matem. izv., 10 (2013), 109–112  mathnet
    32. O. I. Mokhov, “On Commutative Subalgebras of the Weyl Algebra Related to Commuting Operators of Arbitrary Rank and Genus”, Math. Notes, 94:2 (2013), 298–300  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    33. A. B. Zheglov, “On rings of commuting partial differential operators”, St. Petersburg Math. J., 25:5 (2014), 775–814  mathnet  crossref  mathscinet  zmath  isi  elib
    34. V. N. Davletshina, E. I. Shamaev, “On commuting differential operators of rank $2$”, Siberian Math. J., 55:4 (2014), 606–610  mathnet  crossref  mathscinet  isi
    35. Kurke H., Osipov D., Zheglov A., “Commuting Differential Operators and Higher-Dimensional Algebraic Varieties”, Sel. Math.-New Ser., 20:4 (2014), 1159–1195  crossref  isi
    36. Mironov A.E., “Self-Adjoint Commuting Ordinary Differential Operators”, Invent. Math., 197:2 (2014), 417–431  crossref  isi
    37. V. S. Oganesyan, “Commuting differential operators of rank 2 and arbitrary genus $g$ with polynomial coefficients”, Russian Math. Surveys, 70:1 (2015), 165–167  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    38. V. N. Davletshina, “Self-Adjoint Commuting Differential Operators of Rank 2 and Their Deformations Given by Soliton Equations”, Math. Notes, 97:3 (2015), 333–340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    39. A. B. Zheglov, H. Kurke, “Geometric properties of commutative subalgebras of partial differential operators”, Sb. Math., 206:5 (2015), 676–717  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    40. V. N. Davletshina, “Commuting differential operators of rank $2$ with trigonometric coefficients”, Siberian Math. J., 56:3 (2015), 405–410  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    41. V. S. Oganesyan, “Common Eigenfunctions of Commuting Differential Operators of Rank $2$”, Math. Notes, 99:2 (2016), 308–311  mathnet  crossref  crossref  mathscinet  isi  elib
    42. V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Polynomial Coefficients”, Funct. Anal. Appl., 50:1 (2016), 54–61  mathnet  crossref  crossref  mathscinet  isi  elib
    43. V. S. Oganesyan, “On operators of the form $\partial_x^4+u(x)$ from a pair of commuting differential operators of rank 2 and genus $g$”, Russian Math. Surveys, 71:3 (2016), 591–593  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    44. A. E. Mironov, “Self-adjoint commuting differential operators of rank two”, Russian Math. Surveys, 71:4 (2016), 751–779  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    45. A. B. Zheglov, A. E. Mironov, B. T. Saparbayeva, “Commuting Krichever–Novikov differential operators with polynomial coefficients”, Siberian Math. J., 57:5 (2016), 819–823  mathnet  crossref  crossref  isi  elib  elib
    46. Mironov A.E. Zheglov A.B., “Commuting Ordinary Differential Operators with Polynomial Coefficients and Automorphisms of the First Weyl Algebra”, Int. Math. Res. Notices, 2016, no. 10, 2974–2993  crossref  mathscinet  isi  elib  scopus
    47. Pogorelov D.A. Zheglov A.B., “An Algorithm For Construction of Commuting Ordinary Differential Operators By Geometric Data”, Lobachevskii J. Math., 38:6 (2017), 1075–1092  crossref  isi
    48. Davletshina V.N., Mironov A.E., “On Commuting Ordinary Differential Operators With Polynomial Coefficients Corresponding to Spectral Curves of Genus Two”, Bull. Korean. Math. Soc., 54:5 (2017), 1669–1675  crossref  isi
    49. Oganesyan V., “Explicit Characterization of Some Commuting Differential Operators of Rank 2”, Int. Math. Res. Notices, 2017, no. 6, 1623–1640  crossref  isi
    50. V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Rational Coefficients”, Funct. Anal. Appl., 52:3 (2018), 203–213  mathnet  crossref  crossref  mathscinet  isi  elib
    51. A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    52. Vik. S. Kulikov, “On divisors of small canonical degree on Godeaux surfaces”, Sb. Math., 209:8 (2018), 1155–1163  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    53. V. S. Oganesyan, “Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2”, Siberian Math. J., 59:1 (2018), 102–106  mathnet  crossref  crossref  isi  elib
    54. V. S. Oganesyan, “The AKNS hierarchy and finite-gap Schrödinger potentials”, Theoret. and Math. Phys., 196:1 (2018), 983–995  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    55. Oganesyan V., “Matrix Commuting Differential Operators of Rank 2 and Arbitrary Genus”, Int. Math. Res. Notices, 2019, no. 3, 834–851  crossref  isi
    56. Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro, “Commuting Ordinary Differential Operators and the Dixmier Test”, SIGMA, 15 (2019), 101, 23 pp.  mathnet  crossref
    57. Leonid Makar-Limanov, “Centralizers of Rank One in the First Weyl Algebra”, SIGMA, 17 (2021), 052, 13 pp.  mathnet  crossref
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