Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 72, Issue 6, 2007, Pages 817-831

  Liu, Hongyu ^a   Zou, Jun ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Discs and balls; Inverse obstacle scattering; Uniqueness

Indexed keywords

BESSEL FUNCTIONS; POLES AND ZEROS; RESONANCE;

DISCS AND BALLS; INVERSE OBSTACLE SCATTERING; UNIQUENESS;

ACOUSTIC WAVE SCATTERING;

EID: 36549048998     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxm013     Document Type: Article

References (25)

1. ABRAMOWITZ, M. & STEGUN, I. A. (1965) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.
2. ALESSANDRINI, G. & RONDI, L. (2005) Determining a sound-soft polyhedral scatterer by a single far-field measurement. Proc. Am. Math. Soc., 6, 1685-1691 (corrigendum, available at http:// arxiv.org/abs/math.AP/0601406).
3. CHENG, J. & YAMAMOTO, M. (2003) Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves. Inverse Probl., 19, 1361-1384.
4. COLTON, D. & KRESS, R. (1998) Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. Berlin, Germany: Springer.
5. COLTON, D. & SLEEMAN, B. D. (1983) Uniqueness theorems for the inverse problem of acoustic scattering. IMA J. Appl. Math., 31 253-259.
6. ELSCHNER, J. & YAMAMOTO, M. (2006) Uniqueness in determining polygonal sound-hard obstacles with a single incoming wave. Inverse Probl., 22, 355-364.
7. GINTIDES, D. (2005) Local uniqueness for the inverse scattering problem in acoustics via the Faber-Krahn inequality. Inverse Probl. 21, 1195-1205.
8. KIRSCH, A. & KRESS, R. (1993) Uniqueness in inverse obstacle scattering. Inverse Probl., 9, 285-299.
9. KRESS, R. (1995a) Fréchet differentiability of the far field operator for scattering from a crack. J. Inverse III Posed Probl., 3, 305-313.
10. KRESS, R. (1995b) Inverse scattering from an open arc. Math. Methods Appl. Sci., 18, 267-293.
11. LAX, P. D & PHILLIPS, R. S. (1967) Scattering Theory. New York: Academic Press.
12. LEBEDEV, N. N. (1965) Special Functions and Their Applications Englewood Cliffs, NJ: Prentice-Hall.
13. LIU, C. (1997) An inverse obstacle problem: A uniqueness theorem for balls. Inverse Problems in Wave Propagation. Berlin, Germany: Springer, pp. 347-355.
14. LOU, H. Y. & ZOU, J. (2006a) Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers. Inverse Probl., 22, 515-524.
15. LIU, H. Y. & ZOU, J. (2006b) Uniqueness in determining multiple polygonal or polyhedral scatterers of mixed type. Technical Report CUHK-2006-03 (337). Hong Kong: The Chinese University of Hong Kong.
16. LIU, H. Y. & ZOU, J. (2006c) Zeros of Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering problems. Techincal Report CUHK-2007-02 (342). Hong Kong: The Chinese University of Hong Kong.
17. LIU, H. Y. & ZOU, J. (2007) On unique determination of partially coated polyhedral scatterers with far field measurements. Inverse Probl., 23, 297-308.
18. McLEAN, W. (2000) Strongly Elliptic Systems and Boundary Integral Equations. Cambridge: Cambridge University Press.
19. MÖNCH, L. (1997) On the inverse acoustic scattering problem by an open arc: The sound-hard case. Inverse Probl., 13, 1379-1392.
20. OLVER, F. W. J. (1960) Bessel Functions Part III, Zeros and Associated Values. Cambridge: Cambridge University Press.
21. RONDI, L. (2003) Unique determination of non-smooth sound-soft scatters by finitely many far-field measurements. Indiana Univ. Math. J., 6, 1631-1662.
22. SLEEMAN, B. D. (1982) The inverse problem of acoustic scattering. IMA J. Appl. Math., 29, 113-142.
23. TRANTER, C. J. (1968) Bessel Functions with Some Physical Applications. London: English Universities Press.
24. WATSON, G. N. (1944) A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge: Cambridge Press.
25. YUN, K. (2001) The reflection of solutions of Helmholtz equation and an application. Commun. Korean Math. Soc., 16, 427-436.