Abstract
We prove theorems on integral representations of the additive group of a real nuclear space in terms of self-adjoint operators. We assume that algebraic relations are realized in a dense invariant set of integral vectors.
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References
E. Hille, and R. Phillips,Functional Analysis and Semi-Groups, AMS Colloquium Publications V. XXXI, Providence (1957).
A. Devinatz, “A note on semigroups of unbounded self-adjoint operators,”Proc. Amer. Math. Soc.,5, 101–102 (1954).
Yu. M. Berezanskii,Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables, AMS, Providence, Rhole Island (1986).
A. A. Kalyuzhnyi, “On the integral representation of exponentially convex functions,”Ukr. Mat. Zh.,34, No. 3, 370–373 (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.51, No. 2, pp. 271–274, February, 1999.
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Lopotko, O.V. Representations of the additive group of a nuclear space in terms of self-adjoint operators. Ukr Math J 51, 306–310 (1999). https://doi.org/10.1007/BF02513485
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DOI: https://doi.org/10.1007/BF02513485