Rudi Weikard's List of Publications
[Announcements and Surveys|Coauthors|MathSciNet]
1. Research Papers
  1. Inverse spectral and scattering theory for the half-line left definite Sturm-Liouville problem. Jointly with C. Bennewitz and B.M. Brown. To appear in SIAM J. Math. Anal. (2007)
  2. The inverse resonance problem for Hermite operators. Jointly with B.M. Brown and S. Naboko. To appear in Constr. Approx. (2007)
  3. On Inverse Problems for Finite Trees. To appear in the series Operator Theory: Advances and Applications, Vol. 185. Jointly with B.M. Brown. Preprint (2007)
  4. Stability for the inverse resonance problem for a Jacobi operator with complex potential. Inverse problems 23, (2007) 1677-1688. Jointly with M. Marletta. Reprint
  5. Weak stability for an inverse Sturm-Liouville problem with finite spectral data and complex potential. Inverse problems 21, (2005) 1275–1290. Jointly with M. Marletta. Reprint MR:2158108
  6. The inverse resonance problem for Jacobi operators. Bull. London Math. Soc. 37, (2005) 727--737. Jointly with B.M. Brown and S. Naboko. Reprint MR:2164835
  7. A Borg-Levinson theorem for trees. Proc. Royal Soc. Lond. Ser. A. 461, (2005) 3231--3243. Jointly with B.M. Brown. Reprint MR:2172226
  8. A local Borg-Marchenko theorem for difference equations with complex coefficients. In Carlos Conca et al., editors, Partial Differential Equations and Inverse Problems, Contemp. Math. 362, pp. 403--410. Amer. Math. Soc., 2004. dvi MR:2091673
  9. An explicit characterization of Calogero--Moser systems. Trans. Amer. Math. Soc. 358, (2006), 603-656 Jointly with F. Gesztesy and K. Unterkofler. Reprint MR:2177033
  10. The inverse resonance problem for perturbations of algebro-geometric potentials. Inverse problems 20, (2004), 481–494. Jointly with B.M. Brown. Reprint MR:2065435
  11. On the inverse resonance problem. J. LMS 68, (2003), 383-401. Jointly with B.M. Brown and I. Knowles. Reprint MR:1994689
  12. A local Borg-Marchenko theorem for complex potentials. J. Comput. Appl. Math. 148 (2002), 115-131. Jointly with B.M. Brown and R. Peacock. Reprint MR:2003j:81243
  13. On Commuting Matrix Differential Operators. New York J. Math. 8 (2002), 9–30. Original MR:2003d:34188
  14. Floquet Theory for Linear Differential Equations with Meromorphic Solutions. E. J. Qualitative Theory of Diff. Equ., No. 8. (2000), 1-6. Original MR:2001j:34113
  15. On a Theorem of Halphen and its Application to Integrable Systems. J. Math. Anal. Appl. 251 (2000), 504-526. Jointly with F. Gesztesy, K. Unterkofler. Reprint Abstract MR:2001i:37108
  16. On Commuting Differential Operators. Electron. J. Differential Equations 2000 (2000), No. 19, 1-11. Abstract Original MR:2001a:34146
  17. Theta functions on singular hyperelliptic surfaces. Jointly with D. McRae. pdf
  18. On rational and periodic solutions of stationary KdV equations. Doc. Math. J.DMV 4 (1999), 109-126. Reprint Original MR:2000d:35208
  19. A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy. Acta Math. 181 (1998), 63-108. Jointly with F. Gesztesy. Reprint MR:99k:14052
  20. On a theorem of Hochstadt. Math. Ann. 311 (1998), 95-105. Reprint Original MR:99e:34128
  21. On Hill's equation with a singular complex-valued potential. Proc. LMS 76 (1998), 603-633. Reprint MR:99e:34129
  22. On second order linear differential equations with inverse square singularities. In I. Gohberg, R. Mennicken, and C. Tretter, editors, Operator Theory: Advances and Applications, Vol. 102: Differential and Integral Operators, pp. 315-324. Birkhäuser Verlag, 1998. pdf MR:99k:34189
  23. Picard operators. Math. Nachr.  195 (1998), 251-266. Preprint MR:99j:34122
  24. Picard potentials and Hill's equation on a torus. Acta Math. 176 (1996), 73-107. Jointly with F. Gesztesy. Reprint MR:97f:14046
  25. On Picard potentials. Diff. Int. Eq. 8 (1995), 1453-1476. Jointly with F. Gesztesy. MR: 96e:34141
  26. Treibich-Verdier potentials and the stationary (m)KdV hierarchy. Math. Z. 219 (1995), 451-476. Jointly with F. Gesztesy. Reprint MR:96e:14030
  27. Lamé potentials and the stationary (m)KdV hierarchy. Math. Nachr. 176 (1995), 73-91. Jointly with F. Gesztesy. Preprint MR:98a:58086
  28. Gelfand-Dickey- and Drinfeld-Sokolov-type systems. Rev. Math. Phys. 6 (1994), 227-276. Jointly with F. Gesztesy, K. Unterkofler and D. Race. MR:95g:58104
  29. On Gelfand-Dickey systems and inelastic solitons. In W.F. Ames, E.M.Harrell II, and J.V. Herod, editors, Differential Equations with Applications to Mathematical Physics, pp. 325-333. Academic Press, 1993. MR:94b:35241
  30. Spectral deformations and soliton equations. In W.F. Ames, E.M.Harrell II, and J.V. Herod, editors, Differential Equations with Applications to Mathematical Physics, pp. 101-139. Academic Press, 1993. Jointly with F. Gesztesy. MR:93m:34138
  31. On (modified) Boussinesq-type systems and factorizations of associated linear differential expressions. J. LMS 47 (1993), 321-340. Jointly with F. Gesztesy and D. Race. MR:95c:35212
  32. Asymptotically correct lower bound for the sum of negative eigenvalues of Schrödinger operators through a decomposition of unity given by Macke. Asymptotic Analysis 8 (1994), 65-72. Jointly with H. Siedentop. MR:95b:34137
  33. On the absence of a first order correction for the number of bound states of a Schrödinger operator with Coulomb singularity. Comm. PDE. 17 (1992), 615-639. Jointly with B. Helffer, A. Knauf, and H. Siedentop. MR:93h:35149
  34. A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators. Ann. scient. Éc. Norm. Sup. 24 (1991), 215-225. Jointly with H. Siedentop. Reprint MR:92d:81152
  35. On the leading correction of the Thomas-Fermi model: Lower bound. Invent. Math. 97 (1989), 159-193. Jointly with A. M. K. Müller and H. Siedentop. Reprint MR:90k:81285
  36. On the leading energy correction for the statistical model of the atom: Interacting case. Commun. Math. Phys. 112 (1987), 471-490. Jointly with H. Siedentop. Reprint MR:89a:81022
  37. On the leading energy correction for the statistical model of the atom: Non-interacting case. Abh. Braunschweig. Wiss. Ges. 38 (1986), 145-158. Jointly with H. Siedentop.
  38. On some basic properties of density functionals for angular momentum channels. Rep. Math. Phys. 24 (1986), 193-218. Jointly with H. Siedentop. MR:90a:81196
[Research Papers|Coauthors|MathSciNet]
2. Announcements and Surveys
  1. Error estimates for non-selfadjoint inverse Sturm-Liouville problems with finite spectral data. In Spectral Analysis of Differential and Difference Operators, J. Janas, S. Naboko and L.O. Silva eds., Institute of Mathematics, Polish Academy of Sciences, Preprint 35, Seria B. Jointly with M. Marletta. Preprint
  2. Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach. Bull. AMS  35 (1998), 271-317. Jointly with F. Gesztesy. Reprint Original article MR:99i:58075
  3. When is Hill's equation algebro-geometric? In Differential equations, asymptotic analysis, and mathematical physics (Potsdam, 1996), ed. by M. Demuth and B. W. Schulze, pp. 401-406. Math. Res., 100, Akademie Verlag, Berlin, 1997.
  4. Toward a characterization of elliptic solutions of hierarchies of soliton equations. In Applied Analysis (Cont. Math. 221), ed. by J. R. Dorroh, G. Ruiz Goldstein, J. A. Goldstein, and M. M. Tom, AMS, Providence 1998. Jointly with F. Gesztesy. MR:99k:58090
  5. A characterization of elliptic finite-gap potentials. Comptes Rendus Acad. Sci. Paris 321, Série I (1995), 837-841. Jointly with F. Gesztesy. MR:96k:58112
  6. Floquet theory revisited. In Differential Equations and Mathematical Physics, ed. by I. Knowles, pp. 67-84. International Press, 1995. Jointly with F. Gesztesy. MR:2000i:34163
  7. Picard and finite-gap potentials. In Evolution Equations, ed. by G. Ferreyra, G. Ruiz Goldstein, and F. Neubrander, pp. 223-233. Marcel Dekker, 1994. Jointly with F. Gesztesy. MR:95h:35191
  8. Universal behavior of the ground state of large atoms. In Differential Equations and Mathematical Physics: Proceedings of the International Conference held at the University of Alabama at Birmingham, March 15-21, 1990, ed. by C. Bennewitz, pp. 281-293, Boston etc., 1991. Academic Press. Jointly with H. Siedentop. MR:92g:81221
  9. The Scott conjecture in atomic physics. In B.Simon, A.Truman, and I.M. Davies, editors, IX. International Congress on Mathematical Physics, 17-27 July 1988, Swansea, Wales, pp. 306-309, Bristol and New York, 1989. Adam Hilger. Jointly with H. Siedentop. MR:91a:81239
  10. Proof of Scott's conjecture. In Bert-Wolfgang Schulze and Hans Triebel, editors, Symposium "Partial Differential Equations" Holzhau 1988, pp. 295-297, Leipzig, 1989. Teubner-Texte zur Mathematik, Band 112. Jointly with H. Siedentop.
  11. On the leading correction of the statistical atom: Lower bound. Europhys. Lett. 6 (1988), 189-191.  Jointly with H. Siedentop.
  12. Upper bound on the ground state energy of atoms that proves Scott's conjecture. Phys. Lett. A120 (1987), 341-342. Jointly with H. Siedentop. MR:88b:81237


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