Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Schwarz’s lemma and the Szegö kernel function
HTML articles powered by AMS MathViewer

by P. R. Garabedian
Trans. Amer. Math. Soc. 67 (1949), 1-35
DOI: https://doi.org/10.1090/S0002-9947-1949-0032747-8
References
  • Lars V. Ahlfors, Bounded analytic functions, Duke Math. J. 14 (1947), 1–11. MR 21108
  • P. Alexandroff and H. Hopf, Topologie, I, Berlin, 1935. S. Bergman, Partial differential equations, advanced topics, Brown University, Providence, 1941. —, Sur les fonctions orthogonales de plusieurs variables complexes avec les applications à la théorie des fonctions analytiques, Paris, 1947.
  • S. Bergman and M. Schiffer, A representation of Green’s and Neumann’s functions in the theory of partial differential equations of second order, Duke Math. J. 14 (1947), 609–638. MR 22291
  • C. Carathéodory, Über den Variabilitätsbereich der Fourier’schen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo vol. 32 (1911) pp. 193-217.
  • P. R. Garabedian and M. Schiffer, Identities in the theory of conformal mapping, Trans. Amer. Math. Soc. 65 (1949), 187–238. MR 28944, DOI 10.1090/S0002-9947-1949-0028944-8
  • H. Grunsky, Neue Abschätzungen zur konformen Abbildung ein- und mehrfach zusammenhängenden Bereiche, Schriften des Mathematischen Seminars der Universität Berlin vol. 1 (1932) pp. 94-140.
  • Helmut Grunsky, Eindeutige beschränkte Funktionen in mehrfach zusammenhängenden Gebieten. I, Jber. Deutsch. Math.-Verein. 50 (1940), 230–255 (German). MR 3807
  • Maurice H. Heins, Extremal problems for functions analytic and single-valued in a doubly-connected region, Amer. J. Math. 62 (1940), 91–106. MR 686, DOI 10.2307/2371439
  • Maurice H. Heins, On a problem of Walsh concerning the Hadamard three circles theorem, Trans. Amer. Math. Soc. 55 (1944), 349–372. MR 10190, DOI 10.1090/S0002-9947-1944-0010190-0
  • C. Neumann, Vorlesungen über Riemann’s Theorie der Abel’schen Integrale, Leipzig, 1884. R. Nevanlinna, Eindeutige analytische Funktionen, Berlin, 1936.
  • Raphael M. Robinson, Analytic functions in circular rings, Duke Math. J. 10 (1943), 341–354. MR 8092
  • Menahem Schiffer, The span of multiply connected domains, Duke Math. J. 10 (1943), 209–216. MR 8259
  • Menahem Schiffer, The kernel function of an orthonormal system, Duke Math. J. 13 (1946), 529–540. MR 19115
  • F. Schottky, Über die konforme Abbildung mehrfach zusammenhängender ebener Flächen, J. Reine Angew. Math. vol. 83 (1887) pp. 300-351. J. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. Reine Angew. Math. vol. 147 (1917) pp. 205-232 and vol. 148 (1918) pp. 122-145.
  • G. Szegő, Über orthogonale Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören, Math. Z. 9 (1921), no. 3-4, 218–270 (German). MR 1544465, DOI 10.1007/BF01279030
  • J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 30.0X
  • Retrieve articles in all journals with MSC: 30.0X
Bibliographic Information
  • © Copyright 1949 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 67 (1949), 1-35
  • MSC: Primary 30.0X
  • DOI: https://doi.org/10.1090/S0002-9947-1949-0032747-8
  • MathSciNet review: 0032747