Published: 1957 Received: March 15, 1957Available on J-STAGE: August 29, 2006Accepted: -
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Date of correction: August 29, 2006Reason for correction: -Correction: CITATIONDetails: Right : 1) In his Technical Report 17 “On a problem of Hermann Weyl in the theory of singular Sturm Liouville equations,” N. Aronszajn states that he and W. F. Donoghue have obtained results similar to ours. Also M. Rosenblum announces in the abstract 99 in Bull. Amer. Math. Soc. 62 (1956) p. 30 results closely related to ours. (Added in proof) see end of paper. 2) We mean by a subspace a closed linear manifold of _??_. 3) J. v. Neumann, Charakterisierung des Spektrums eines Integraloperators, Actualités scientifique et industrielles, 229, Paris, 1935. 4) K. Friedrichs, On the perturbation of continuous spectra, Communications on Pure and Applied Mathematics 1 (1948), pp. 361-406; Ueber die Spektralzerlegung eines Integraloperators, Math. Ann. 115 (1938), pp. 249-272. 5) F. J. Murray and J. v. Neumann, On rings of operators, Ann. Math. 37 (1936), pp. 116-229. 6) S0 corresponds to what is called the scattering operator in quantum mechanics, where H0 and H1 represent unperturbed and perturbed Hamiltonians of the mechanical system. Here it is usual that M0 coincides with _??_ so that S0 is unitary. 7) See e. g. R. Nevanlinna, Eindeutige analytische Funktion, Berlin, 1936. 8) M. H. Stone, Linear transformations in Hilbert space, New York, 1932, 9) E. C. Titchmarsh, Theory of Fourier integrals, Oxford, 1948.
Date of correction: August 29, 2006Reason for correction: -Correction: PDF FILEDetails: -