Resonances — Models and Phenomena pp 78-104 | Cite as
Perturbation theory for resonances in terms of fredholm determinants
II Mathematical Framework
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Keywords
Point Interaction Fredholm Determinant Meromorphic Continuation Geometric Multiplicity Pure Coulomb
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References
- [1]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions” (Dover, New York, 1972)Google Scholar
- [2]S. Albeverio and R. Høegh-Krohn, J. Operator Theory 6, 313 (1981)Google Scholar
- [3]S. Albeverio, F. Gesztesy and R. Høegh-Krohn, Ann. Inst. H. Poincaré A37, 1 (1982)Google Scholar
- [4]S. Albeverio, F. Gesztesy, R. Høegh-Krohn and L. Streit, Ann. Inst. H. Poincaré A 38, 263 (1983)Google Scholar
- [5]S. Albeverio, D. Bollé, F. Gesztesy, R. Høegh-Krohn and L. Streit, Ann. Phys. 148, 308 (1983)CrossRefGoogle Scholar
- [6]S. Albeverio, L.S. Ferreira, F. Gesztesy, R. Høegh-Krohn and L. Streit, Phys. Rev. C29, 680 (1984)Google Scholar
- [7]S. Albeverio and R. Høegh-Krohn, “Perturbation theory of resonances in auantum mechanics”, J. Math. Anal. Appl. 100 (1984), in printGoogle Scholar
- [8]S. Albeverio, F. Gesztesy, R. Høegh-Krohn and W. Kirsch, “On point interactions in one dimension”, J. Operator Theory, 12, 101 (1984)Google Scholar
- [9]S. Albeverio, F. Gesztesy, H. Holden'and R. Høegh-Krohn, “Solvable Models in Quantum Mechanics”, book in preparationGoogle Scholar
- [10]A.A. Arsenev, Theoret. Math. Phys. 15, 505 (1973)CrossRefGoogle Scholar
- [11]D. Babbitt and E. Balslev, J. Math. Anal. Appl. 54, 316 (1976)CrossRefGoogle Scholar
- [12]E. Balslev, “Resonances in three-body scattering theory”, Aarhus Preprint Series 1981/82, No. 3Google Scholar
- [13]E. Balslev, “Local spectral deformation techniques for Schrödin-ger operators”, Preprint 1982Google Scholar
- [14]H. Baumgärtel, M. Demuth and M. Wollenberg, Math. Nachr. 86, 167 (1978)Google Scholar
- [15]D. Bollé and S.F.J. Wilk, J. Math. Phys. 24, 1555 (1983)CrossRefGoogle Scholar
- [16]D. Bollé, F. Gesztesy and S.F.J. Wilk, “A complete treatment of low-energy scattering in one dimension”, J. Operator Theory, in printGoogle Scholar
- [17]D. Bollé, F. Gesztesy and W. Schweiger, “Scattering theory for long-range systems at threshold”, Univ. Bielefeld, ZiF-Preprint 1984, No. 76Google Scholar
- [18]D. Bollé, C. Daneels, F. Gesztesy and S.F.J. Wilk, in preparationGoogle Scholar
- [19]D. Bollé, F. Gesztesy, C. Nessmann and L. Streit, in preparationGoogle Scholar
- [20]E. Brüning and F. Gesztesy, J. Math. Phys. 24, 1516 (1983)CrossRefGoogle Scholar
- [21]K. Chadan and P.C. Sabatier, “Inverse Problems in Quantum Scattering Theory” (Springer, New York 1977)Google Scholar
- [22]M. Cheney, J. Math. Phys. 25, 95 (1984)Google Scholar
- [23]M. Cheney, “Two-dimensional scattering: The number of bound states from scattering data”, Stanford preprintGoogle Scholar
- [24]M. Ciafaloni and P. Menotti, Nuovo Cimento 35, 160 (1965)Google Scholar
- [25]J.M. Combes, Int. J. Quantum Chem. 14, 353 (1978)CrossRefGoogle Scholar
- [26]L. Dabrowski and H. Grosse, “on nonlocal point interactions in one, two and three dimensions”, Preprint, Univ. Vienna, UWThPh-1983-15Google Scholar
- [27]E.B. Davies, Lett. Math. Phys. 1, 31 (1975)CrossRefGoogle Scholar
- [28]C.L. Dolph, J.B. McLeod and D. Thoe, J. Math. Anal. Appl. 16, 311 (1966)Google Scholar
- [29]N. Dunford and J.T. Schwartz, “Linear Operators II. Spectral Theory” (Interscience, New York, 1963)Google Scholar
- [30]G. Flamand, “Mathematical theory of non-relativistic two-and three-particle systems with point interactions”, Cargése Lectures, F. Lurcat(ed.) (Gordon and Breach, New York, 1967)Google Scholar
- [31]R. Froese, I. Herbst, M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, J. Anal. Math. 41, 272 (1982)Google Scholar
- [32]F. Gesztesy and L. Pittner, Rep. Math. Phys. 19, 143 (1984)CrossRefGoogle Scholar
- [33]A. Grossmann and T.T. Wu, J. Math. Phys. 2, 710 (1961)CrossRefGoogle Scholar
- [34]A. Grossmann, J. Math. Phys: 2, 714 (1961)CrossRefGoogle Scholar
- [35]A. Grossmann and T.T. Wu, J. Math. Phys. 3, 684 (1962)CrossRefGoogle Scholar
- [36]A. Grossmann, R. Høegh-Krohn and M. Mebkhout, J. Math. Phys. 21, 2377 (1980)Google Scholar
- [37]E.M., Harrell, Commun. Math. Phys. 86, 221 (1982)CrossRefGoogle Scholar
- [38]H. Holden, “On coupling constant thresholds in two dimensions”, Univ. Bielefeld, ZiF-Preprint 1984, No. 44Google Scholar
- [39]H. Holden, R. Høegh-Krohn and S. Johannesen, Adv. Appl. Math. 4, 402 (1983)Google Scholar
- [40]H. Holden, R. Høegh-Krohn and M. Mebkhout, “The short-range expansion for multiple well scattering theory”, Preprint, CNRS-Marseille, CPT-84/PE.1590Google Scholar
- [41]L.P. Horwitz and I.M. Siegal, Helv. Phys. Acta 51, 685 (1978)Google Scholar
- [42]L. Hostler, J. Math. Phys. 8, 642 (1967)CrossRefGoogle Scholar
- [43]J.S. Howland, Proc. Am. Math. Soc. 21, 381 (1969)Google Scholar
- [44]J.S. Howland, Arch. Rat. Mech. Anal. 39, 323 (1970)CrossRefGoogle Scholar
- [45]J.S. Howland, Proc. Am. Math. Soc. 28, 177 (1971)Google Scholar
- [46]J.S. Howland, J. Math. Anal. Appl. 36, 12 (1971)Google Scholar
- [47]J.S. Howland, Pac. J. Math. 55,157 (1974)Google Scholar
- [48]J.S. Howland, J. Math. Anal. Appl. 50, 415 (1975)CrossRefGoogle Scholar
- [49]A. Jensen, J. Math. Anal. Appl. 59, 505 (1977)CrossRefGoogle Scholar
- [50]A. Jensen, Ann. Inst. H. Poincaré A33,209 (1980)Google Scholar
- [51]A. Jensen and T. Kato, Duke Math. J. 46, 583 (1979)CrossRefGoogle Scholar
- [52]R. Jost, Helv. Phys. Acta 20, 256 (1947)Google Scholar
- [53]R. Jost and A. Pais, Phys. Rev. 82, 840 (1951)CrossRefGoogle Scholar
- [54]T. Kato, “Perturbation Theory for Linear Operators”, 2nd ed. (Springer, New York, 1980)Google Scholar
- [55]T. Kato, Math. Ann. 162, 258 (1966)CrossRefGoogle Scholar
- [56]N.N. Khuri, Phys. Rev. 107, 1148 (1957)CrossRefGoogle Scholar
- [57]M. Klaus, Ann. Phys. 108, 288 (1977)CrossRefGoogle Scholar
- [58]M. Klaus, Helv. Phys. Acta 55, 49 (1982)Google Scholar
- [59]M. Klaus and B. Simon, Ann. Phys. 130, 251 (1980)CrossRefGoogle Scholar
- [60]R. Konno and S.T. Kuroda, J. Fac. Sci. Univ. Tokyo 113, 55 (1966)Google Scholar
- [61]S.N. Lakaev, Theoret. Math. Phys. 44, 810 (1980)Google Scholar
- [62]J.B. McLeod, Quart. J. Math. Oxford 18, 219 (1967)Google Scholar
- [63]K. Meetz, J. Math. Phys. 3, 690 (1962)CrossRefGoogle Scholar
- [64]M. Murata, J. Func. Anal. 49, 10 (1982)CrossRefGoogle Scholar
- [65]R.G. Newton, “Scattering Theory of Waves and Particles”, 2nd ed. (Springer, New York, 1982)Google Scholar
- [66]R.G. Newton, J. Math. Phys. 13, 880 (1972)CrossRefGoogle Scholar
- [67]R.G. Newton, Czech. J. Phys. B24, 1195 (1974)CrossRefGoogle Scholar
- [68]R.G. Newton, J. Math. Phys. 18, 1348 (1977)CrossRefGoogle Scholar
- [69]R.G. Newton, J. Math. Phys. 18, 1582 (1977)CrossRefGoogle Scholar
- [70]H.M. Nussenzveig, Nucl. Phys. 11, 499 (1959)CrossRefGoogle Scholar
- [71]J. Nuttall, J. Math. Phys. 8, 873 (1967)CrossRefGoogle Scholar
- [72]A.G. Ramm, J. Math. Anal. Appl. 88, 1 (1982)CrossRefGoogle Scholar
- [73]J. Rauch, J. Func. Anal. 35, 304 (1980)Google Scholar
- [74]M. Reed and B. Simon, “Methods of Modern Mathematical Physics III: Scattering Theory” (Academic, New York, 1979)Google Scholar
- [75]M. Reed and B. Simon, “Methods of Modern Mathematical Physics IV: Analysis of Operators” (Academic, New York 1978)Google Scholar
- [76]F. Rellich, Math. Z. 49, 702 (1943/44)CrossRefGoogle Scholar
- [77]H. Rollnik, Z. Physik 145, 639 (1956)CrossRefGoogle Scholar
- [78]N. Shenk and D. Thoe, Rocky Mountain J. Math. 1 89 (1971)Google Scholar
- [79]H.K.H. Siedentop, Phys. Lett. 99A, 65 (1983)Google Scholar
- [80]H.K.H. Siedentop, “On the width of resonances”, Caltech-Preprint 1984Google Scholar
- [81]B. Simon, “Quantum Mechanics for Hamiltonians defined as Quadratic Forms” (Princeton Univ. Press 1971)Google Scholar
- [82]B. Simon, Ann. Math. 97, 247 (1974)Google Scholar
- [83]B. Simon, Ann. Phys. 97, 279 (1976)CrossRefGoogle Scholar
- [84]B. Simon, Adv. Math. 24, 244 (1977)Google Scholar
- [85]B. Simon, Int. J. Quantum Chem. 14, 529 (1978)CrossRefGoogle Scholar
- [86]B. Simon, “Trace Ideals and their Applications”, London Math. Soc. Lecture Notes Series 35 (Cambridge Univ. Press 1979)Google Scholar
- [87]S. Steinberg, Arch. Rat. Mech. Anal. 38, 278 (1970)Google Scholar
- [88]J. Zorbas, J. Math. Phys. 21, 840 (1980)CrossRefGoogle Scholar
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