Abstract
It is shown that if a sequence with finitely many negative squares has a uniquely determined minimal definitizing polynomial, then it is determinate in the sense of Krein and Langer.
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References
Akhiezer, N.I.: The classical moment problem and some related questions in analysis. Edinburgh: Oliver and Boyd 1965.
Berg, C., Christensen, J.P.R. and P.H. Maserick: Sequences with finitely many negative squares. To appear in J. Functional Ana-lysis.
Buchwalter, H., Cassier, G.: Mesures canoniques dans le problème classique des moments. Ann. Inst. Fourier 34,2 (1984), 45–52.
Iohvidov, I.S., Krein, M.G.: Spectral theory of operators in spaces with an indefinite metric I,II. Amer. Math. Soc. Transl. (2), 13 (1960), 105–175 and (2) 34 (1963), 283–373.
Iohvidov, I.S., Krein, M.G. and H. Langer: Introduction to the spectral theory of operators in spaces with an indefinite metric. Berlin: Akademie-Verlag 1982.
Krein, M.G., Langer, H.: The spectral function of a self-adjoint operator in a space with indefinite metric. Soviet Math. Dokl. 4 (1963), 1236–1239.
Krein, M.G., Langer, H.: Defect subspaces and generalized resolvents of a hermitian operator in the space Πκ.Functional Anal. Appl. 5 (1971), 136–146, 217–228.
Krein, M.G., Langer, H.: Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zu-sammenhängen. I. Einige Funktionenklassen und ihre Darstellungen. Math. Nachr. 77 (1977), 187–236. II. Verallgemeinerte Resolventen, u-Resolventen und ganze Operatoren. J. Functional Analysis 30 (1978), 390–447.
Krein, M.G., Langer, H.: On some extension problems which are closely connected with the theory of hermitian operators in a space Πκ. III. Indefinite analogues of the Hamburger and Stieltjes moment problems. Beiträge zur Analysis 14 (1979), 25–40, 15 (1981), 27–45.
Lo, C.-Y.; A class of polynomials in self-adjoint operators in spaces with an indefinite metric. Canad. J. Math. 20 (1968), 673–678.
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© 1988 Springer-Verlag
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Berg, C. (1988). On the uniqueness of minimal definitizing polynomials for a sequence with finitely many negative squares. In: Eymard, P., Pier, JP. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086590
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DOI: https://doi.org/10.1007/BFb0086590
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