Construction of Principal Functions by Orthogonal Projection
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 887-896

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Given a point set E on an open Riemann surface V we denote by H(E) the space of functions u harmonic in open sets O(u) containing E. Let V0 be a regular region of V with border α, and consider restrictions f to α of functions in H(α). For V1 = V — ⊽0, an operator L from H(α) to H(⊽1) is, by definition, normal if 1 2 3 4 5
Nakai, Mitsuru; Sario, Leo. Construction of Principal Functions by Orthogonal Projection. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 887-896. doi: 10.4153/CJM-1966-089-4
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[1] 1. Ahlfors, L. V., Remarks on Riemann surfaces, Lectures on functions of a complex variable (Ann Arbor, 1955), pp. 45–48. Google Scholar

[2] 2. Ahlfors, L. V. and Sario, L., Riemann surfaces (Princeton, N.J., 1960). Google Scholar

[3] 3. Browder, F. E., Principal functions for elliptic systems of differential equations, Bull. Amer. Math. Soc, 71 (1965), 342–344. Google Scholar

[4] 4. Constantinescu, C. and Cornea, A., Ideale Ränder Riemannscher Flächen (Berlin, 1963). Google Scholar

[5] 5. Oikawa, K., A remark to Sario's lemma on harmonic functions, Proc. Amer. Math. Soc., 11 (1960), 425–428. Google Scholar

[6] 6. Oikawa, K., A constant related to harmonic functions, Japan. J. Math., 29 (1959), 111–113. Google Scholar

[7] 7. Rodin, B., Reproducing kernels and principal functions, Proc. Amer. Math. Soc., 13 (1962), 982–992. Google Scholar

[8] 8. Sario, L., Existence des fonctions d'allure donnée sur une surface de Riemann arbitraire, C. R. Acad. Sci. Paris, 229 (1949), 1293–1295. Google Scholar

[9] 9. Sario, L., A linear operator method on arbitrary Riemann surfaces, Trans. Amer. Math. Soc., 72 (1952), 281–295. Google Scholar

[10] 10. Sario, L., An integral equation and a general existence theorem for harmonic functions, Comment. Math. Helv., 38 (1964), 284–292. Google Scholar

[11] 11. Sario, L., Schiffer, M., and Glasner, M., The span and principal functions in Riemannian spaces, J. Analyse Math., 15 (1965), 115–134. Google Scholar

[12] 12. Sario, L. and Weill, G., Normal operators and uniformly elliptic self-adjoint partial differential equations, Trans. Amer. Math. Soc., 120 (1965), 225–235. Google Scholar

[13] 13. Weill, G., Capacity differentials on open Riemann surfaces, Pacific J. Math., 12 (1962), 769–776. Google Scholar

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