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11.and also in the English translation Generalized Functions (Academic, New York, 1964), Vol. 4.
12.S. K. Berberian, Notes on Spectral Theory (Van Nostrand, New York, 1966); the relevant theorems are found in Chap. 4.
13.We note that, in both the case of projectivity and the case of decomposability, whenever an indefinite metric is introduced, then is both symmetric and η symmetric; that is, we have both and for f and g in the domain of To have a renormalized T which is η symmetric but not symmetric requires the renormalized Hilbert space to have contributions from singularities of that lie off the real axis; we have not pursued this problem.
14.J. A. Shohat and J. D. Tomarkin, The Problem of Moments (American Mathematical Society, Providence, R.I., 1943); we are here making use of Lemma 2.1, p. 23.
15.See Ref. 14, Lemma 2.2, p. 24.
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