- Kirk , J.G. and Schneider , P. 1987 . On the acceleration of charged particles at relativistic shock fronts . Astrophysical J. , 315 : 425 – 433 .
- Bednarz , J. and Ostrowski , M. 1998 . Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves . Physical Review Letters , 80 (18) : 3911 – 3914 .
- Kirk , J.G. , Guthmann , A.W. , Galant , Y.A. and Achtenberg , A. 2000 . Particle acceleration at ultrarelativistic shocks: an eigenfunction method . Astrophysical J. , 542 : 235 – 242 .
- Bothe , W. 1929 . Die Streuabsorption der Elektronenstrahlen . Zeitschr. f. Physik , 54 : 161 – 178 .
- Veling , E.J.M. 1984 . Asymptotic analysis of a singular Sturm-Liouville boundary value problem . Integral Equations and Operator Theory , 7 : 561 – 587 .
- Langer , R.E. 1935 . On the asymptotic solutions of ordinary differential equations . Trans. Amer. Math. Soc. , 37 : 397 – 416 .
- Eberhard , W. , Freiling , G. and Schneider , A. 1994 . Connection formulas for second-order differential equations with a complex parameter and having an arbitrary number of turning points . Mathem. Nachr. , 165 : 205 – 229 .
- Kaper , H.G. , Kwong , M.K. , Lekkerkerker , C.G. and Zettl , A. 1983 . Full- and half-range theory of indefinite Sturm-Liouville problems , 55 Argonne National Laboratory . ANL-83-76
- Beats , R. 1985 . Indefinite Sturm-Liouville problems and half-range completeness . J. Differ. Equations , 56 : 391 – 407 .
- Dorodnicyn , A.A. 1960 . Asymptotic laws of distribution of the characteristic values for certain special forms of differential equations of the second order . Amer. Math. Soc. Translations , 16 : 1 – 101 . (Ser. 2)
- McHugh , J. 1970 . An historical survey of ordinary linear differential equations with a large parameter and turning points . Arch. Hist. Exact. Sci. , 7 : 277 – 324 .
- Daho , K. and Langer , H. 1977 . Sturm-Liouville operators with an indefinite weight functions . Proc. Roy. Soc. Edinburgh , 78A : 161 – 191 .
- Wasow , W. 1985 . Linear Turning Point Theory , Berlin : Springer .
- Freiling , G. and Yurko , V.A. 1997 . Inverse problems for differential equations with turning points . Inverse Problems , 13 : 1247 – 1263 .
- Freiling , G. and Yurko , V.A. 1999 . Inverse spectral problems for differential equations on the half-line with turning points . J. Diff. Equations , 154 : 419 – 453 .
- Eberhard , W. , Freiling , G. and Wilcken-Stoeber , K. 2001 . Indefinite eigenvalue problems with several singular points and turning points . Math. Nachr. , 229 : 51 – 71 .
- Krein , S.G. , Petunin , Y.I. and Semenov , E.M. 1978 . Interpolation of Linear Operators , Moscow : Nauka . English transi. (1982), Amer. Math. Soc. Providence
- M. Vietri. On the universality of the spectrum of particles accelerated at relativistic shocks (to appear).
- Dubrovskii , V.V. and Tipko , A.N. 2001 . On the uniqueness of the solution of an inverse problem of spectral analysis for a singular second-order ODE . Russian Math. Surveys , 56 (3)
- Conway , J.B. 1995 . Functions of One Complex Variable, , 2nd Edn. , Vol. I , New York : Springer-Verlag .
- Marchenko , V.A. 1972 . Spectral Theory of Sturm-Liouville Operators , Kiev : Naukova Dumka .
- Keldysh , M.V. 1971 . On the completeness of eigenfunctions of some clasees of non-selfadjoint linear operators . Russian Math. Surveys , 26 : 15 – 44 .
- Mennicken , R. and Möller , M. 1984 . Root functions, eigenvectors, associated vectors and the inverse of a holomorphic operator function . Arch. Math. , 42 : 455 – 463 .
- Freiling , G. and Yurko , V.A. 2001 . Inverse Sturm-Liouville Problems and their Applications , New York : NOVA .
- Yurko , V. A. 2000 . Inverse Spectral Problems for Differential Operators and their Applications , New York : Gordon and Breach .
- Choose new content alerts to be informed about new research of interest to you
- Easy remote access to your institution's subscriptions on any device, from any location
- Save your searches and schedule alerts to send you new results
- Export your search results into a .csv file to support your research