Half-range expansions for an astrophysical problem

Letters in Mathematical Physics

Volumn 64, Issue 1, 2003, Pages 65-73

  Freiling, G ^a   Vietri, M ^b   Yurko, V ^c  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b SCUOLA NORMALE SUPERIORE   (Italy)

^c SARATOV STATE UNIVERSITY   (Russian Federation)

Author keywords

astrophysical shocks; boundary value problems; full and half range expansion theorems; particle acceleration

Indexed keywords

EID: 9744272440     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024943620249     Document Type: Article

References (13)

1. Beals, R.: Indefinite Sturm-Liouville problems and half-range completeness, J. Differential Equations 56 (1985), 391-407.
2. Bednarz, J. and Ostrowski, M.: Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves, Phys. Rev. Lett. 80 (1998), 3911-3914.
3. Bothe, W.: Die Streuabsorption der Elektronenstrahlen, Zeit. Phys. 54 (1929), 161-178.
4. Curgus, B. and Langer, H.: A Krein space approach to symmetric ordinary differential operators with an indefinite weight function, J. Differential Equations 79 (1989), 31-61.
5. Freiling, G., Rykhlov, V. S. and Yurko, V. A.: Spectral analysis for an indefinite singular Sturm-Liouville problem, Appl. Anal. 81 (2002), 1283-1305.
6. Freiling, G. and Yurko, V. A.: Inverse Sturm-Liouville Problems and their Applications, NOVA Science Publishers, New York, 2001.
7. Kaper, H. G., Kwong, M. K., Lekkerkerker, C. G. and Zettl, A.: Full- and half-range theory of indefinite Sturm-Liouville problems, Preprint, Argonne National Laboratory, ANL-83-76 (1983).
8. Kirk, J. G., Guthmann, A. W., Galant, Y. A. and Achtenberg, A.: Particle acceleration at ultrarelativistic shocks: an eigenfunction method, Astrophys. J. 542 (0000), 235-242.
9. Kirk, J. G. and Schneider, P.: On the acceleration of charged particles at relativistic shock fronts, Astrophys. J. 315 (1987), 425-433.
10. Krein, S. G., Petunin, Y. I. and Semenov E. M.: Interpolation of Linear Operators, Nauka, Moscow, 1978; English transl., Amer. Math. Soc., Providence, 1982.
11. Veling, E. J. M.: Asymptotic analysis of a singular Sturm-Liouville boundary value problem, Integral Equations Operator Theory 7 (1984), 561-587.
12. Vietri, M.: On particle acceleration around shocks. I, Astrophys. J. 591 (2003), 530-539.
13. Young, R. M.: An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980.