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References
N. I. Achieser,Vorlesungen über Approximationstheorie Akademie Verlag (Berlin, 1953).
N. I. Achieser, Über einige Funktionen, welche in zwei gegebenen Intervallen am wenigsten von Null abweichen,Bull. Acad. Sci. URSS, VII. 5. Nr. 9 (1932), 1163–1202.
N. I. Achieser, Über eine Eigenschaft der „elliptischen” Polynome,Comm. Kharkov Math. Soc.,9 (1934), 3–8.
N. I. Achieser, Yu. Ya. Tomčuk, On the theory of orthogonal polynomials over several intervals,Soviet Math. Dokl.,2 (1961), 687–690.
P. Barrucand, D. Dickinson, On cubic transformations of orthogonal polynomials,Proc. Amer. Math. Soc.,17 (1966), 810–814.
B. C. Carlson and J. Todd, Zolotarev's first problem — the best approximation by polynomials of degree ≦n−2 tox n −nσx n −1 in [−1, +1],Aequationes Math.,26 (1983), 1–33.
W. Gautschi, An algorithmic implementation of the generalized Christoffel theorem, in “Numerical Integration”, pp. 89–106 (Proc. Inst. Oberwolfach, 1981), ISNM 57, Birkhäuser (Basel, 1982).
J. S. Geronimo, W. Van Assche, Orthogonal polynomials with asymptotically periodic recurrence coefficients,J. Approx. Theory,46 (1986), 251–283.
Ya. L. Geronimus, On some finite difference equations and corresponding systems of orthogonal polynomials,Zap. Mat. Otd. Fiz.-Mat. Fak. i Kharkov Mat. Obsc.,25 (1957), 87–100.
E. I. Krupickii, On a class of polynomials deviating least from zero on two intervals,Soviet Math. Dokl.,2 (1961), 657–660.
N. Levinson, Simplified treatment of integrals of Cauchy type, the Hilbert problem and singular integral equations,SIAM Rev.,7 (1965), 474–502.
A. Magnus, Recurrence coefficients for orthogonal polynomials on connected and nonconnected sets, in “Padé Approximation and its Applications”, pp. 150–171 (Proc. Antwerp., 1979), Lecture Notes in Mathematics 765, Springer, Berlin, 1979.
J. Nuttall, S. R. Singh, Orthogonal polynomials and Padé approximants associated with a system of arcs,J. Approx. Th.,21 (1977), 1–42.
F. Peherstorfer, Extremalpolynome in derL 1- undL 2-Norm auf zwei disjunkten Intervallen, in „Approximation Theory and Functional Analysis”, pp. 269–280 (Proc. Inst. Oberwolfach, 1983), ISNM 65, Birkhäuser (Basel, 1984).
F. Peherstorfer, Orthogonal polynomials inL 1-approximation, to appear inJ. Approx. Th.
F. Peherstorfer On Tchebycheff polynomials on disjoint intervals, Colloq. Math. Soc. Bolyai, 49. Haar Mem. Conf., Budapest, 1985, pp. 737–751.
O. Perron,Die Lehre von den Kettenbrüchen, Teubner, 2th ed. (Leipzig/Berlin, 1929).
A. Pinkus, Z. Ziegler, Interlacing properties of the zeros of the error function in bestL P -aproximations,J. Approx. Th.,27 (1978), 1–18.
P. Turchi, F. Ducastelle, G. Treglia, Band gaps and asymptotic behaviour of continued fraction coefficients,J. Phys.,C15 (1982), 2891–2924.
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Parts of this paper were written while, the author was visiting the Center for Approximation Theory, Texas A&M University, College Station, Texas. The author wishes also to acknowledge the support of the Max Kade Foundation.
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Peherstorfer, F. Orthogonal- and Chebyshev polynomials on two intervals. Acta Math Hung 55, 245–278 (1990). https://doi.org/10.1007/BF01950935
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DOI: https://doi.org/10.1007/BF01950935