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Schwarz lemma

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1: 1.10 Functions of a Complex Variable
Schwarz Reflection Principle
Schwarz’s Lemma
2: 1.7 Inequalities
Cauchy–Schwarz Inequality
Cauchy–Schwarz Inequality
3: 17.12 Bailey Pairs
Weak Bailey Lemma
Strong Bailey Lemma
4: 2.3 Integrals of a Real Variable
§2.3(ii) Watson’s Lemma
(In other words, differentiation of (2.3.8) with respect to the parameter λ (or μ ) is legitimate.) … Watson’s lemma can be regarded as a special case of this result. For error bounds for Watson’s lemma and Laplace’s method see Boyd (1993) and Olver (1997b, Chapter 3). … The first result is the analog of Watson’s lemma2.3(ii)). …
5: 1.8 Fourier Series
Riemann–Lebesgue Lemma
6: 2.4 Contour Integrals
§2.4(i) Watson’s Lemma
If this integral converges uniformly at each limit for all sufficiently large t , then by the Riemann–Lebesgue lemma1.8(i)) …
7: Bibliography G
  • M. B. Green, J. H. Schwarz, and E. Witten (1988a) Superstring Theory: Introduction, Vol. 1. 2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • M. B. Green, J. H. Schwarz, and E. Witten (1988b) Superstring Theory: Loop Amplitudes, Anomalies and Phenomenolgy, Vol. 2. 2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • 8: 10.11 Analytic Continuation
    9: 6.12 Asymptotic Expansions
    10: Bibliography
  • G. E. Andrews and A. Berkovich (1998) A trinomial analogue of Bailey’s lemma and N = 2 superconformal invariance. Comm. Math. Phys. 192 (2), pp. 245–260.
  • G. E. Andrews (2001) Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.