Publications by Rudi Weikard
2022
[74]S. Redolfi, R. Weikard, "Green's functions for first-order systems of ordinary differential equations without the unique continuation property", Integral Equations Operator Theory, 2022. [bibtex] [url] [doi]
[73]M. Nguyen, R. Weikard, "Asymptotic behavior of eigenvalues for first order systems with distributional coefficients", submitted, 21 pages, 2022. [bibtex] [pdf]
[72]M. Nguyen, R. Weikard, "Comparison and oscillation theorems for first order systems with distributional coefficients", submitted, 11 pages, 2022. [bibtex] [pdf]
[71]A. Ghatasheh, R. Weikard, "Sign-changing points of solutions of homogeneous Sturm–Liouville equations with measure-valued coefficients", Appl. Anal., vol. 101, no. 5, 2022, pp. 1556–1570. [MR:4410825] [bibtex] [pdf] [doi]
[70]K. Campbell, R. Weikard, "On the spectral theory of systems of first order equations with periodic distributional coefficients", in From Complex Analysis to Operator Theory: A Panorama In Memory of Sergey Naboko, M. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, I. Wood, Eds., Birkhäuser, 2022. [bibtex] [pdf]
2021
[69]K. Campbell, M. Nguyen and R. Weikard, "On the spectral theory for first-order systems without the unique continuation property", Linear Multilinear Algebra, vol. 69, no. 12, 2021, pp. 2315–2323. [MR:4298818] [bibtex] [pdf] [doi]
2020
[68]C. Bennewitz, M. Brown and R. Weikard, Spectral and scattering theory for ordinary differential equations. Vol. I, Springer, Cham, 2020. [MR:4199125] [bibtex] [url] [doi]
[67]A. Ghatasheh, R. Weikard, "Spectral theory for systems of ordinary differential equations with distributional coefficients", J. Differential Equations, vol. 268, no. 6, 2020, pp. 2752–2801. [MR:4047968] [bibtex] [url] [doi]
2019
[66]F. Gesztesy, S. N. Naboko, R. Weikard, M. Zinchenko, "Donoghue-type m-functions for Schrödinger operators with operator-valued potentials", J. Anal. Math., vol. 137, no. 1, 2019, pp. 373–427. [MR:3938008] [bibtex] [pdf] [doi]
2017
[65]A. Ghatasheh, R. Weikard, "On Leighton's comparison theorem", J. Differential Equations, vol. 262, no. 12, 2017, pp. 5978–5989. [MR:3624546] [bibtex] [pdf] [doi]
2016
[64]C. Bennewitz, B. M. Brown and R. Weikard, "The spectral problem for the dispersionless Camassa-Holm equation", in Operator theory, function spaces, and applications, Birkhäuser/Springer, Cham, 2016, pp. 67–90. [MR:3617001] [bibtex] [pdf] [doi]
2015
[63]M. Bledsoe, R. Weikard, "The inverse resonance problem for left-definite Sturm-Liouville operators", J. Math. Anal. Appl., vol. 423, no. 2, 2015, pp. 1753–1773. [MR:3278226] [bibtex] [pdf] [doi]
2014
[62]F. Gesztesy, R. Weikard, "Some remarks on the spectral problem underlying the Camassa-Holm hierarchy", in Operator theory in harmonic and non-commutative analysis, Birkhäuser/Springer, Cham, 2014, pp. 137–188. [MR:3134550] [bibtex] [pdf] [doi]
2013
[61]F. Gesztesy, R. Weikard and M. Zinchenko, "Initial value problems and Weyl-Titchmarsh theory for Schrödinger operators with operator-valued potentials", Oper. Matrices, vol. 7, no. 2, 2013, pp. 241–283. [MR:3099184] [bibtex] [pdf] [doi]
[60]R. Shterenberg, R. Weikard and M. Zinchenko, "Stability for the inverse resonance problem for the CMV operator", in Spectral analysis, differential equations and mathematical physics: a festschrift in honor of Fritz Gesztesy's 60th birthday, Amer. Math. Soc., Providence, RI, 2013, pp. 315–326. [MR:3087912] [bibtex] [url]
[59]R. AlAhmad, R. Weikard, "On inverse problems for left-definite discrete Sturm-Liouville equations", Oper. Matrices, vol. 7, no. 1, 2013, pp. 35–70. [MR:3076458] [bibtex] [pdf] [doi]
[58]F. Gesztesy, R. Weikard and M. Zinchenko, "On spectral theory for Schrödinger operators with operator-valued potentials", J. Differential Equations, vol. 255, no. 7, 2013, pp. 1784–1827. [MR:3072671] [bibtex] [url] [doi]
[57]F. Gesztesy, R. Weikard and M. Zinchenko, "On a class of model Hilbert spaces", Discrete Contin. Dyn. Syst., vol. 33, no. 11-12, 2013, pp. 5067–5088. [MR:3060827] [bibtex] [pdf]
2012
[56]C. Bennewitz, B. M. Brown and R. Weikard, "Scattering and inverse scattering for a left-definite Sturm–Liouville problem", J. Differential Equations, vol. 253, no. 8, 2012, pp. 2380–2419. [MR:2950456] [bibtex] [pdf] [doi]
[55]M. Marletta, S. Naboko, R. Shterenberg, R. Weikard, "On the inverse resonance problem for Jacobi operators—uniqueness and stability", J. Anal. Math., vol. 117, 2012, pp. 221–247. [MR:2944096] [bibtex] [pdf] [doi]
[54]C. Bennewitz, B. M. Brown and R. Weikard, "A uniqueness result for one-dimensional inverse scattering", Math. Nachr., vol. 285, no. 8-9, 2012, pp. 941–948. [MR:2928391] [bibtex] [pdf] [doi]
2010
[53]R. Weikard, M. Zinchenko, "The inverse resonance problem for CMV operators", Inverse Problems, vol. 26, no. 5, 2010, pp. 055012, 10. [MR:2647154] [bibtex] [pdf] [doi]
[52]M. Marletta, R. Shterenberg and R. Weikard, "On the inverse resonance problem for Schrödinger operators", Comm. Math. Phys., vol. 295, no. 2, 2010, pp. 465–484. [MR:2594334] [bibtex] [pdf] [doi]
2009
[51]B. M. Brown, R. Weikard, "On inverse problems for finite trees", in Methods of spectral analysis in mathematical physics, Basel: Birkhäuser Verlag, 2009, pp. 31–48. [MR:2732071] [bibtex] [pdf]
[50]B. M. Brown, S. Naboko and R. Weikard, "The inverse resonance problem for Hermite operators", Constr. Approx., vol. 30, no. 2, 2009, pp. 155–174. [MR:2519659] [bibtex] [pdf] [doi]
[49]C. Bennewitz, B. M. Brown and R. Weikard, "Inverse spectral and scattering theory for the half-line left-definite Sturm-Liouville problem", SIAM J. Math. Anal., vol. 40, no. 5, 2009, pp. 2105–2131. [MR:2471914] [bibtex] [pdf]
2007
[48]M. Marletta, R. Weikard, "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, L. Silva, Eds., Institute of Mathematics, Polish Academy of Sciences, 2007, pp. 9–18. [bibtex] [pdf]
[47]M. Marletta, R. Weikard, "Stability for the inverse resonance problem for a Jacobi operator with complex potential", Inverse Problems, vol. 23, no. 4, 2007, pp. 1677–1688. [MR:2348728] [bibtex] [pdf]
2006
[46]F. Gesztesy, K. Unterkofler and R. Weikard, "An explicit characterization of Calogero-Moser systems", Trans. Amer. Math. Soc., vol. 358, no. 2, 2006, pp. 603–656 (electronic). [MR:2177033] [bibtex] [pdf]
2005
[45]B. M. Brown, R. Weikard, "A Borg-Levinson theorem for trees", Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., vol. 461, no. 2062, 2005, pp. 3231–3243. [MR:2172226] [bibtex] [pdf]
[44]B. M. Brown, S. Naboko and R. Weikard, "The inverse resonance problem for Jacobi operators", Bull. London Math. Soc., vol. 37, no. 5, 2005, pp. 727–737. [MR:2164835] [bibtex] [pdf]
[43]M. Marletta, R. Weikard, "Weak stability for an inverse Sturm-Liouville problem with finite spectral data and complex potential", Inverse Problems, vol. 21, no. 4, 2005, pp. 1275–1290. [MR:2158108] [bibtex] [pdf]
2004
[42]R. Weikard, "A local Borg-Marchenko theorem for difference equations with complex coefficients", in Partial differential equations and inverse problems, Providence, RI: Amer. Math. Soc., 2004, pp. 403–410. [MR:2091673] [bibtex] [pdf]
[41]B. M. Brown, R. Weikard, "The inverse resonance problem for perturbations of algebro-geometric potentials", Inverse Problems, vol. 20, no. 2, 2004, pp. 481–494. [MR:2065435] [bibtex] [pdf]
2003
[40]B. M. Brown, I. Knowles and R. Weikard, "On the inverse resonance problem", J. London Math. Soc. (2), vol. 68, no. 2, 2003, pp. 383–401. [MR:1994689] [bibtex] [pdf]
2002
[39]B. M. Brown, R. A. Peacock and R. Weikard, "A local Borg-Marchenko theorem for complex potentials", J. Comput. Appl. Math., vol. 148, no. 1, 2002, pp. 115–131. [MR:1946191] [bibtex] [pdf]
[38]R. Weikard, "On commuting matrix differential operators", New York J. Math., vol. 8, 2002, pp. 9–30 (electronic). [MR:1887696] [bibtex] [html]
2000
[37]R. Weikard, "Floquet theory for linear differential equations with meromorphic solutions", Electron. J. Qual. Theory Differ. Equ., 2000, pp. No. 8, 6 pp. (electronic). [MR:1797880] [bibtex] [pdf]
[36]F. Gesztesy, K. Unterkofler and R. Weikard, "On a theorem of Halphen and its application to integrable systems", J. Math. Anal. Appl., vol. 251, no. 2, 2000, pp. 504–526. [MR:1794755] [bibtex] [pdf] [doi]
[35]R. Weikard, "On commuting differential operators", Electron. J. Differential Equations, 2000, pp. No. 19, 11 pp. (electronic). [MR:1744086] [bibtex] [html]
1999
[34]R. Weikard, "On rational and periodic solutions of stationary KdV equations", Doc. Math., vol. 4, 1999, pp. 107–126 (electronic). [MR:1683290] [bibtex] [pdf]
[33]F. Gesztesy, R. Weikard, "Toward a characterization of elliptic solutions of hierarchies of soliton equations", in Applied analysis (Baton Rouge, LA, 1996), Providence, RI: Amer. Math. Soc., 1999, pp. 133–161. [MR:99k:58090] [bibtex] [pdf]
1998
[32]M. Ohmiya, R. Weikard, "DDT method for Lamé-Ince potentials and modular functions", in Research Meeting Report 9ME-S2: New developments of soliton theory, Research Institute of Applied Mathematics, Kyushu University, 1998. [bibtex]
[31]F. Gesztesy, R. Weikard, "A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy", Acta Math., vol. 181, no. 1, 1998, pp. 63–108. [MR:99k:14052] [bibtex] [pdf]
[30]R. Weikard, "Picard operators", Math. Nachr., vol. 195, 1998, pp. 251–266. [MR:99j:34122] [bibtex] [pdf]
[29]F. Gesztesy, R. Weikard, "Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies—an analytic approach", Bull. Amer. Math. Soc. (N.S.), vol. 35, no. 4, 1998, pp. 271–317. [MR:99i:58075] [bibtex] [pdf]
[28]R. Weikard, "On second order linear differential equations with inverse square singularities", in Differential and integral operators (Regensburg, 1995), Basel: Birkhäuser, 1998, pp. 315–324. [MR:99k:34189] [bibtex] [pdf]
[27]R. Weikard, "On a theorem of Hochstadt", Math. Ann., vol. 311, no. 1, 1998, pp. 95–105. [MR:99e:34128] [bibtex] [pdf]
[26]R. Weikard, "On Hill's equation with a singular complex-valued potential", Proc. London Math. Soc. (3), vol. 76, no. 3, 1998, pp. 603–633. [MR:99e:34129] [bibtex] [pdf]
1997
[25]D. McRae, R. Weikard, "Theta functions on singular hyperelliptic surfaces", 1997. [bibtex] [pdf]
[24]R. Weikard, "When is Hill's equation algebro-geometric?", in Differential equations, asymptotic analysis, and mathematical physics (Potsdam, 1996), Berlin: Akademie Verlag, 1997, pp. 401–406. [MR:1456207] [bibtex]
1996
[23]F. Gesztesy, R. Weikard, "Picard potentials and Hill's equation on a torus", Acta Math., vol. 176, no. 1, 1996, pp. 73–107. [MR:97f:14046] [bibtex] [pdf]
1995
[22]F. Gesztesy, R. Weikard, "Floquet theory revisited", in Differential equations and mathematical physics (Birmingham, AL, 1994), Int. Press, Boston, MA, 1995, pp. 67–84. [MR:1703573] [bibtex] [pdf]
[21]F. Gesztesy, R. Weikard, "Lamé potentials and the stationary (m)KdV hierarchy", Math. Nachr., vol. 176, 1995, pp. 73–91. [MR:98a:58086] [bibtex] [pdf]
[20]F. Gesztesy, R. Weikard, "A characterization of elliptic finite-gap potentials", C. R. Acad. Sci. Paris Sér. I Math., vol. 321, no. 7, 1995, pp. 837–841. [MR:96k:58112] [bibtex]
[19]F. Gesztesy, R. Weikard, "Treibich-Verdier potentials and the stationary (m)KdV hierarchy", Math. Z., vol. 219, no. 3, 1995, pp. 451–476. [MR:96e:14030] [bibtex] [pdf]
[18]F. Gesztesy, R. Weikard, "On Picard potentials", Differential Integral Equations, vol. 8, no. 6, 1995, pp. 1453–1476. [MR:96e:34141] [bibtex] [pdf]
[17]F. Gesztesy, R. Weikard, "Picard and finite-gap potentials", in Evolution equations (Baton Rouge, LA, 1992), New York: Dekker, 1995, pp. 223–233. [MR:95h:35191] [bibtex]
1994
[16]F. Gesztesy, D. Race, K. Unterkofler, R. Weikard, "On Gel$'$fand-Dickey and Drinfel$'$d-Sokolov systems", Rev. Math. Phys., vol. 6, no. 2, 1994, pp. 227–276. [MR:95g:58104] [bibtex] [pdf]
[15]H. Siedentop, R. Weikard, "Asymptotically correct lower bound for the sum of negative eigenvalues of Schrödinger operators through a decomposition of unity given by Macke", Asymptotic Anal., vol. 8, no. 1, 1994, pp. 65–72. [MR:95b:34137] [bibtex]
1993
[14]F. Gesztesy, D. Race and R. Weikard, "On (modified) Boussinesq-type systems and factorizations of associated linear differential expressions", J. London Math. Soc. (2), vol. 47, no. 2, 1993, pp. 321–340. [MR:1207952] [bibtex] [pdf] [doi]
[13]R. Weikard, "On Gelfand-Dickey systems and inelastic solitons", in Differential equations with applications to mathematical physics, Boston, MA: Academic Press, 1993, pp. 325–333. [MR:94b:35241] [bibtex] [pdf]
[12]F. Gesztesy, R. Weikard, "Spectral deformations and soliton equations", in Differential equations with applications to mathematical physics, Boston, MA: Academic Press, 1993, pp. 101–139. [MR:93m:34138] [bibtex] [pdf]
1992
[11]B. Helffer, A. Knauf, H. Siedentop, R. Weikard, "On the absence of a first order correction for the number of bound states of a Schrödinger operator with Coulomb singularity", Comm. Partial Differential Equations, vol. 17, no. 3-4, 1992, pp. 615–639. [MR:93h:35149] [bibtex] [pdf]
[10]H. Siedentop, R. Weikard, "Universal behavior of the ground state of large atoms", in Differential equations and mathematical physics (Birmingham, AL, 1990), Boston, MA: Academic Press, 1992, pp. 281–293. [MR:92g:81221] [bibtex]
1991
[9]H. Siedentop, R. Weikard, "A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators", Ann. Sci. École Norm. Sup. (4), vol. 24, no. 2, 1991, pp. 215–225. [MR:92d:81152] [bibtex] [pdf]
1989
[8]H. Siedentop, R. Weikard, "On the leading correction of the Thomas-Fermi model: lower bound", Invent. Math., vol. 97, no. 1, 1989, pp. 159–193. [MR:90k:81285] [bibtex] [pdf]
[7]H. Siedentop, R. Weikard, "Proof of Scott's conjecture", in Symposium "Partial Differential Equations" (Holzhau, 1988), Leipzig: Teubner, 1989, pp. 295–297. [MR:1105819] [bibtex] [pdf]
[6]H. Siedentop, R. Weikard, "The Scott conjecture in atomic physics", in IXth International Congress on Mathematical Physics (Swansea, 1988), Bristol: Hilger, 1989, pp. 306–309. [MR:91a:81239] [bibtex] [pdf]
1988
[5]H. Siedentop, R. Weikard, "On the leading correction of the statistical atom: lower bound", Europhys. Lett., vol. 6, 1988, pp. 189–191. [bibtex] [pdf]
1987
[4]H. Siedentop, R. Weikard, "On the leading energy correction for the statistical model of the atom: interacting case", Comm. Math. Phys., vol. 112, no. 3, 1987, pp. 471–490. [MR:908549] [bibtex] [pdf]
[3]H. Siedentop, R. Weikard, "Upper bound on the ground state energy of atoms that proves Scott's conjecture", Phys. Lett. A, vol. 120, no. 7, 1987, pp. 341–342. [MR:881781] [bibtex]
1986
[2]H. K. H. Siedentop, R. Weikard, "On some basic properties of density functionals for angular momentum channels", Rep. Math. Phys., vol. 24, no. 2, 1986, pp. 193–218. [MR:941720] [bibtex] [pdf]
[1]H. K. H. Siedentop, R. Weikard, "On the leading energy correction for the statistical model of the atom: Non-interacting case", Abh. Braunschweig. Wiss. Ges., vol. 38, 1986, pp. 145-158. [bibtex] [pdf]
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