By Theodore S Chihara, Mathematics

Topics comprise the illustration theorem and distribution services, persevered fractions and chain sequences, the recurrence formulation and homes of orthogonal polynomials, certain capabilities, and a few particular structures of orthogonal polynomials. quite a few examples and workouts, an in depth bibliography, and a desk of recurrence formulation complement the text.

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Suppose that the boundary of the domain is a rectifiable Jordan curve # which consists of a finite number of smooth arcs on each of which the inclination is a uniformly Holder continuous function of the arc length. Let Λ and λ be upper bounds for the Holder constants and exponents, respectively, 31 32 PAUL W. BERG for the inclination, and let Γ denote a positive lower bound for the ratio of chord length to arc length on #. Let ^ have corners at the points zf at which the interior angles are ytn, 0 < yt ^ 2, / = 1, 2, .

7(1954), 441-504. 3. L. " Wiley, New York, 1958. 4. L. , Volume 2. Chelsea, Bronx, New York, 1945. 5. G. Birkhoff and E. " Academic Press, New York, 1957. 6. D. Gilbarg, Jets and cavities, in "Encyclopedia of Physics," (S. ), Volume9, "Fluid Dynamics" 3. Springer-Verlag, Berlin and New York, 1960. 7. J. Leray, Les problèmes de representation conforme d'Helmholtz, Comment. Math. Helv. 8 (1935-1936), 149, 250. 8. K. Löwner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, Math.

These facts are essentially well known, although perhaps they have not been written down in such detail. Our purpose here is to make the paper essentially self-contained, without requiring any substantial knowledge of Lie groups or symmetric spaces. In Section 3 we classify the conjugacy classes of elements in U(\9 n\ F). We thereby obtain analogs of the elliptic, parabolic, and loxodromic transformations in PSL(2, C). In Section 4 we classify the connected Lie subgroups of C/(l, n, F) and use this result to prove discreteness theorems.