×

Spectral and scattering theory for Dirac operators. (English) Zbl 0297.47008


MSC:

47A40 Scattering theory of linear operators
35J10 Schrödinger operator, Schrödinger equation
35P25 Scattering theory for PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alsholm, P., & G. Schmidt, Spectral and scattering theory for Schrödinger operators. Arch. Rational Mech. Anal. 40, 281-311 (1971). · Zbl 0226.35076 · doi:10.1007/BF00252679
[2] Birman, M. Sh., On the spectra of singular boundary value problems. Mat. Sb. 55, 125-174 (1961), in Russian (English translation: A. 17. S. Transi. Ser. 2, Vol. 53, 23-80).
[3] Birman, M. Sh, Scattering problems for differential operators with constant coefficients. Funkcional Anal, i Prilo?en 3, No. 3, 1-16 (1969), in Russian. · Zbl 0249.34035 · doi:10.1007/BF01078269
[4] Howland, J. S., On the essential spectrum of Schrödinger operators with singular potentials. Pac. J. Math. 25, 533-542 (1968). · Zbl 0194.45104
[5] Kato, T., Perturbation theory for linear operators, Berlin Heidelberg New York: Springer 1966. · Zbl 0148.12601
[6] Kato, T., Wave operators and similarity for some non self-adjoint operators. Math. Ann. 162, 255-279 (1966). · Zbl 0139.31203 · doi:10.1007/BF01360915
[7] Kato, T., & S. T. Kuroda, The abstract theory of scattering. Rocky Mountain Jour. of Math. 1, 127-171 (1971). · Zbl 0241.47005 · doi:10.1216/RMJ-1971-1-1-127
[8] Kato, T., & S. T. Kuroda, Theory of Simple Scattering and Eigenfunction Expansions, Functional Analysis and Related Fields (Edited by Felix E. Browder). Berlin Heidelberg New York: Springer 1970. · Zbl 0224.47004
[9] Konno, R., & S. T. Kuroda, On the finiteness of perturbed eigenvalues. Journ. of Fac. of Science, Univ. of Tokyo, Sec. I., Vol. XIII, Part 1, 55-63 (1964). · Zbl 0149.10203
[10] Kuroda, S. T., Construction of eigenfunction expansions by the perturbation method and its application to n-dimensional Schrödinger operators. M.R.C. Technical Summary Report No. 744, Univ. of Wisconsin (1967). · Zbl 0154.16401
[11] Kuroda, S. T., Perturbation of eigenfunction expansions. Proc. Nat. Acad. Sc., 57, No. 5, 1213-1217 (1967). · Zbl 0154.16401 · doi:10.1073/pnas.57.5.1213
[12] Mochizuki, K., On the perturbation of the continuous spectrum of the Dirac operator Proc. Japan Acad. 40, No. 9, 707-712 (1964). · Zbl 0131.12602 · doi:10.3792/pja/1195522600
[13] Prosser, R. T., Relativistic potential scattering. J. Math. Phys. 4, 1048-1054 (1963). · Zbl 0128.22004 · doi:10.1063/1.1704033
[14] Thomson, M., Eigenfunction expansions and the associated scattering theory for potential perturbations of the Dirac equation. Quarterly Journal of Mathematics 23, 17-55 (1972). · Zbl 0229.35070 · doi:10.1093/qmath/23.1.17
[15] Watson, G., A Treatise on the Theory of Bessel Functions, 2nd edition. Cambridge Univ. Press 1952. · Zbl 0046.30604
[16] Wilcox, C., Measurable eigenvectors for hermitian matrix-valued polynomials. Technical Summary Report No. 10, Dept. of Math., Univ. of Denver (1970). · Zbl 0223.35080
[17] Yamada, O., On the principle of limiting absorption for the Dirac operator. RIMS, Kyoto Univ. 8, 557-577 (1972/73). · Zbl 0257.35009 · doi:10.2977/prims/1195192961
[18] Jörgens, K., Perturbations of the Dirac Operator. Proceedings of the Dundee Conference on Differential Equations 1972. Berlin Heidelberg New York: Springer (to appear). · Zbl 0245.35070
[19] Gustafson, K. E., & P. A. Rejto, Some essentially self-adjoint Dirac operators with spherically symmetric potentials. Israel J. of Math. 14, No. 1, 63-75 (1973). · Zbl 0255.47017 · doi:10.1007/BF02761535
[20] Rejto, P. A., On the essential spectrum of the hydrogen energy and related operators. Pac. J. of Math. 19, 109-140 (1966). · Zbl 0144.17701
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.