Analytic Theory of Continued Fractions

By T. B., H. Wall. 2000

1,120 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c561d6effef8cf9417b49dfaf955d89de98de6f1

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Citations in the corpus

Sum rules for Jacobi matrices and their applications to spectral theory (2001, positive): “An alternate way of recovering J from µ is the continued fraction expan- sion for the function mµ(z) near infinity, (1.5) mµ(E) = 1 −E + b1 − a21 −E + b2 + · · · .”
On the Classification of Rational Knots (2002, neutral): “See for example [17], [23], [18], [47].”
Random walks on co-compact fuchsian groups (2013, neutral): “, [36]), for any two real numbers x1 < x2, neither of which is an atom of ν,”
Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015, background): “Key later work is by Wallis and Euler [178] (see the Notes to Section 9.2 for a capsule biography).”
Matrix measures, moment spaces and Favard's theorem for the interval [0,1] and [0,∞) (2002, background): “It was further discovered by Wall [33] that µ is supported on the interval [0, 1] if and only if the coefficients ζk form a chain sequence; that is, they can further be decomposed as ζk = qk−1pk, (1.6) where qk = 1 − pk (q0 = 1) and 0 < pk < 1.”
Synthesis of Narrowband Reflection-Type Phasers With Arbitrary Prescribed Group Delay (2012, background): “1A Hurwitz polynomial is a polynomial whose coefficients are positive real numbers or, equivalently, whose zeros are located in the left half-plane of the complex Laplace plane [21], [22].”
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms (2011, neutral): “I-4, or [32], Theorem 50.”
Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials (2009, background): “[27], [30] ), the Jacobi-Perron VCF (25) can be transformed to a Stieltjes VCF (for details, see [3] ).”
Fractional Kinetics in Kac–Zwanzig Heat Bath Models (2004, positive): “Another class of problems is when κ̂(p) has a continued fraction representation in the form of a Jacobi fraction [49]: ̂̃ κ(p) = ∆1 p + α1 + ∆2 p + α2 + ∆3 p + α3 + .”