Geodesic
Separating Singularities of Holomorphic Functions
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 473-477

Voir la notice de l'article provenant de la source Cambridge University Press

We present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results for other classes of functions.
DOI : 10.4153/CMB-1998-061-x
Mots-clés : 30E99, 30E10 
Müller, Jürgen; Wengenroth, Jochen. Separating Singularities of Holomorphic Functions. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 473-477. doi: 10.4153/CMB-1998-061-x
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[1] 1. Aronszajn, N., Sur les décompositions des fonctions analytiques uniformes et sur leur applications. Acta Math. 65 (1935), 1–156. Google Scholar

[2] 2. Bonilla, A. and Fariña, J. C., Elliptic fusion lemma. Math. Japon. 41 (1995), 441–445. Google Scholar

[3] 3. Dufresnoy, A., Gauthier, P. M. and Ow, W. H., Uniform approximation on closed sets by solutions of elliptic partial differential equations. Complex Variables Theory Appl. 6 (1986), 235–247. Google Scholar

[4] 4. Gaier, D., Remarks on Alice Roth's fusion lemma. J. Approx. Theory 37 (1983), 246–250. Google Scholar

[5] 5. Gaier, D., Lectures on Complex Approximation. Birkhäuser, Boston, 1987. Google Scholar

[6] 6. Garnett, J., Analytic Capacity and Measure. Springer, Berlin, 1972. Google Scholar

[7] 7. Hörmander, L., An Introduction to Complex Analysis in Several Variables. 3rd edn, North-Holland, Amsterdam, 1990. Google Scholar

[8] 8. Kalton, N. J., Peck, N. T. and Roberts, J.W., An F-Space Sampler. Cambridge University Press, Cambridge, 1984. Google Scholar

[9] 9. Nersesjan, A., Alice Roth's fusion lemma. Soviet J. Contemporary Math. Anal. 23 (1988), 34–47. Google Scholar

[10] 10. Roth, A., Uniform and tangential approximation by meromorphic functions on closed sets. Canad. J. Math. 28 (1976), 104–111. Google Scholar

[11] 11. Rudin, W., Functional Analysis. McGraw-Hill, New York, 1973. Google Scholar

[12] 12. Schmieder, G., Fusion lemma and boundary structure. J. Approx. Theory 71 (1992), 305–311. Google Scholar

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