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Inequalities for the Solutions of Linear Integral Equations
1.A. P. Balachandran, “Criteria for the Solubility of Partial‐Wave Dispersion Relations,” Syracuse University preprint (1965) and Ann. Phys. (to be published).
2.For example, they can be used in the study of the Lippmann‐Schwinger equation in potential scattering which, it is known from the work of Coester and of Scadron, Weinberg, and Wright, can be rewritten as an integral equation with an ‐kernel for all energies if the potential is sufficiently well‐behaved.
2.See F. Coester, Phys. Rev. 133, B1516 (1964);
2.and M. Scadron, S. Weinberg, and J. Wright, Phys. Rev. 135, B202 (1964). This would then lead to bounds for the T‐matrix or for its norm in terms of the potential. Another application is to partial‐wave dispersion relations [cf. Ref. 1].
3.This result was pointed out by Professor E. C. G. Sudarshan.
4.See, for example, F. Riesz and B. Sz.‐Nagy, Functional Analysis (Fredrick Ungar Publishing Company, New York, 1955), p. 83.
5.See, for example, Ref. 4, p. 40.
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