Point interactions in acoustics: One-dimensional models

Journal of Mathematical Physics

Volumn 47, Issue 6, 2006, Pages

  Cacciapuoti, C ^a   Figari, R ^a   Posilicano, A ^b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF INSUBRIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745683216     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2209553     Document Type: Article

References (20)

1. Albeverio, S., Gesztesy, F., Høegh-Krohn, R., and Holden, H., Solvable Models in Quantum Mechanics, 2nd ed. (AMS Chelsea, Providence, RI, 2005).
2. Dirac, P. A. M., "Classical theory of radiating electrons," Proc. R. Soc. London, Ser. A 167, 148-169 (1938).
3. Gorbachuk, V. I. and Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations (Kluwer Academic, Amsterdam, 1991).
4. Griffiths, D. J. and Steinke, C. A., "Waves in locally periodic media," Am. J. Phys. 69, 137-154 (2001).
5. infeld, L. and Wallace, P. R., "The equation of motion in electrodynamics," Phys. Rev. 57, 797-806 (1940).
6. Kijowski, J., "Electrodynamics of moving particles," Gen. Relativ. Gravit. 26, 167-201 (1994).
7. Marino, M., "Classical electrodynamics of point charges," Ann. Phys. 301, 85-127 (2002).
8. Noja, D. and Posilicano, A., "The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle," Ann. Inst. Henri Poincare, Sect. A 68, 351-377 (1998).
9. Noja, D. and Posilicano, A. "On the point limit of the Pauli-Fierz model," Ann. Inst. Henri Poincare, Sect. A 71, 425-457 (1999).
10. Posilicano, A., "A Kreln-like formula for singular perturbations of self-adjoint operators and applications," J. Funct. Anal. 183, 109-147 (2001).
11. Posilicano, A., "Singular perturbations of abstract wave equations," J. Funct. Anal, (in press).
12. Reed, M. and Simon, B., Methods of Modern Mathematical Physics. Vol 1; Functional Analysis (Academic, New York, 1972).
13. Reed, M. and Simon, B., Methods of Modem Mathematical Physics. Vol 2: Fourier Analysis, Self-Adjointness (Academic, New York, 1975).
14. Reed, M. and Simon, B., Methods of Modern Mathematical Physics. Vol 3: Scattering Theory (Academic, New York, 1979).
15. Reed, M. and Simon, B., Methods of Modern Mathematical Physics. Vol 4: Analysis of Operators (Academic, New York, 1978).
16. Soffer, A. and Weinstein, M. I., "Nonautonomous Hamiltonians," J. Stat. Phys. 93, 359-391 (1998a).
17. Soffer, A. and Weinstein, M. I., "Time dependent resonances theory," Geom. Funct. Anal. 8, 1-43 (1998b).
18. Soffer, A. and Weinstein, M. I., "Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations," Invent. Math. 136, 9-74 (1999).
19. Spohn, H., Dynamics of Charged Particles and their Radiation Field (Cambridge University Press, Cambridge, 2004).
20. Templin, J. D., "Radiation reaction and runaway solutions in acoustics," Am. J. Phys. 67, 407-413 (1999).