A non-standard boundary value problem related to geomagnetism

Quarterly of Applied Mathematics

Volumn 62, Issue 3, 2004, Pages 423-457

  Kaiser, Ralf ^a   Neudert, Michael ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; GEOMAGNETISM; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; POLES AND ZEROS; POLYNOMIALS; THEOREM PROVING; VECTORS;

GEOMAGNETIC FIELD; HILBERT SPACE; LAPLACE EQUATION; LEGENDRE POLYNOMIALS;

BOUNDARY VALUE PROBLEMS;

EID: 4944229222     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/2086038     Document Type: Article

References (19)

1. Abramowitz, M., Stegun, I. A. (eds): Handbook of mathematical functions, Dover Publications, New York 1972.
2. Backus, G. E.: Application of a non-linear boundary-value problem for Laplace's equation to gravity and geomagnetic intensity surveys, Quart. J. Mech. Appl. Math. 21, 195-221 (1968).
3. Backus, G. E.: Non-uniqueness of the external geomagnetic field determined by surface intensity measurements, J. Geophys. Res. 75, 6339-6341 (1970).
4. Bloxham, J., Jackson, A.: Fluid flow near the surface of earth's outer core, Reviews of Geophysics 29, 1, 97-120 (1991).
5. Boas, R. P.: Expansions of analytic functions, Transactions of the American Mathematical Society 48, 467-487 (1940).
6. Courant, R., Hilbert, D.: Methods of Mathematical Physics, vol II, chapter IV, §1, Interscience Publishers, New York 1962.
7. Hide, R.: Frozen vector fields and the inverse problem of inferring motions in the electrically-conducting fluid core of a planet from observations of secular changes in its main magnetic field, in: The Physics of the Planets, The Royal Astronomical Society, 1986.
8. Hulot, G., Khokhlov, A., Le Mouël, J. L.: Uniqueness of mainly dipolar magnetic fields recovered from directional data, Geophys. J. Int. 129, 347-354 (1997).
9. Kakeya, S.: On the limits of the roots of an algebraic equation with positive coefficients, Tôhoku Math. J. 2, 140-142 (1912).
10. Kellogg, O. D.: Foundations of Potential Theory, Berlin, Heidelberg, New York 1967.
11. Kono, M.: Uniqueness problems in the spherical harmonic analysis of the geomagnetic field direction data, J. Geomag. Geoelectr. 28, 11-29 (1976).
12. Merrill, R. T., McElhinny, M. W.: The Earth's Magnetic Field (Its History, Origin and Planetary Perspective), Academic Press, London 1983.
13. de Sz. Nagy, B.: Expansion Theorems of Paley-Wiener-Type, Duke Math. J. 14, 975-978 (1947).
14. Paley, R., Wiener, N.: Fourier Transforms in the Complex Domain, The American Mathematical Society, New York 1973.
15. Protter, R. P., Weinberger, H. R.: Maximum Principles in Differential Equations, Springer, New York 1984.
16. Proctor, M. R. E., Gubbins, D.: Analysis of geomagnetic directional data, Geophys. J. Int. 100, 69-77 (1990).
17. Riordan, J.: Combinatorial Identities, Huntington, New York 1979.
18. Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik II, 2nd ed., Berlin, Heidelberg, New York 1978.
19. Varshalovich, D. A., Moskalev, A. N., Khersonskii, V. K.: Quantum Theory of Angular Momentum, World Scientific, Singapore, New Jersey, Hong Kong