×

zbMATH — the first resource for mathematics

Algebro-geometric Schrödinger operators in many dimensions. (English) Zbl 1153.14303
Summary: We collect known results about the Schrödinger operators \(L= - \Delta +u(x)\), generalizing to higher dimension those algebro-geometric operators \(L= - d^{2}/dx^{2}+u(x)\) with rational, trigonometric and elliptic potential which appear in the finite-gap theory.

MSC:
14H70 Relationships between algebraic curves and integrable systems
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
35J10 Schrödinger operator, Schrödinger equation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] COMMUN MATH PHYS 61 pp 1– (1978)
[2] COMM PURE APPL MATH 30 pp 95– (1977)
[3] COMMUN MATH PHYS 190 pp 113– (1997)
[4] RUSSIAN MATH SURVEYS 53 pp 208– (1998)
[5] LETT MATH PHYS 52 pp 103– (2000)
[6] DUKE MATH J 118 pp 279– (2003)
[7] TRANS GROUPS 2 pp 31– (1997)
[8] THEOR MATH PHYS 109 pp 1269– (1997)
[9] RUSSIAN MATH SURVEYS 53 pp 167– (1998)
[10] J MATH PHYS 41 pp 5139– (2000)
[11] ADV MATH 166 pp 193– (2002)
[12] PHYS. LETT. A 267 pp 256– (2000)
[13] COMMUN MATH PHYS 126 pp 597– (1990)
[14] COMMUN MATH PHYS 152 pp 29– (1993)
[15] PHYS. LETT. A 285 pp 339– (2001)
[16] COMMUN MATH PHYS 206 pp 533– (1999)
[17] COMMUN MATH PHYS 239 pp 115– (2003)
[18] COMMUN MATH PHYS 169 pp 441– (1995)
[19] Doklady Akademii Nauk. Rossiyskaya Akademiya Nauk 229 pp 15– (1976)
[20] COMMUN MATH PHYS 103 pp 177– (1986)
[21] MOSC MATH J 2 pp 555– (2002)
[22] COMPOSIT MATH 114 pp 125– (1998)
[23] J NONLIN MATH PHYS 12 pp 95– (2005)
[24] IMRN 2002 pp 521– (2002)
[25] IMRN 2003 pp 2487– (2003)
[26] COMPOSIT MATH 107 pp 143– (1997)
[27] MATH ANN 294 pp 295– (1992)
[28] ACTA MATH 176 pp 73– (1996)
[29] PHYS. LETT. A 246 pp 97– (1998)
[30] LETT MATH PHYS 17 pp 11– (1989)
[31] TEORET MAT FIZ 23 pp 51– (1975)
[32] Physica. D 152 153 pp 66– (2001)
[33] RUSSIAN MATH SURVEYS 32 pp 180– (1977)
[34] FUNKTS ANALIZ I EGO PRILOZHEN 14 pp 45– (1980) · Zbl 0455.14011 · doi:10.1007/BF01078418
[35] RUSSIAN MATH SURVEYS 50 pp 1101– (1995)
[36] DUKE MATH J 62 pp 315– (1991)
[37] AM J MATH 116 pp 65– (1994)
[38] FUNKTS ANALIZ I EGO PRIL 8 pp 54– (1974)
[39] THEOR MATH PHYS 121 pp 1574– (1999)
[40] PHYS REPORTS 94 pp 313– (1983)
[41] J MATH SCI UNIV TOKYO 2 pp 1– (1995)
[42] IZV MATH 65 pp 941– (2001)
[43] PROC STEKLOV INST MAT 224 pp 291– (1999)
[44] COMMUN ALGEBRA 29 pp 4157– (2001)
[45] DUKE MATH J 84 pp 565– (1996)
[46] COMMUN MATH PHYS 110 pp 191– (1987)
[47] IHES PUBL 61 pp 5– (1985) · Zbl 0592.35112 · doi:10.1007/BF02698802
[48] COMMUN MATH PHYS 245 pp 249– (2004)
[49] RUSSIAN MATH SURVEYS 56 pp 1107– (2001)
[50] THE GROTHENDIECK FESTSCHRIFT VOL vol. 88 pp 437– (1990)
[51] Doklady Akademii Nauk. Rossiyskaya Akademiya Nauk 279 pp 20– (1984)
[52] Doklady Akademii Nauk. Rossiyskaya Akademiya Nauk 279 pp 784– (1984)
[53] THEOR MATH PHYS 94 pp 253– (1993)
[54] RUSSIAN MATH SURVEYS 51 pp 573– (1996)
[55] DOC MATH 4 pp 107– (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.