A measure-theoretical approach to the nuclear and inductive spectral theorems
Copyright policy )A measure-theoretical approach to the nuclear and inductive spectral theorems
In the present article, a revision of fundamental results concerning Gelfand-Kostyuchenko rigged Hilbert space is given. In particular, the authors give new versions of inductive and nuclear spectral theorems, which provide an explicit expression for generalized eigenvectors of normal operators in terms of certain Radon-Nikodym differentiation of a measure of the direct integral (which is the spectral representation of the Hilbert space on which a normal operator acts) by measures generated by an ordered set of cyclic vectors from the Hilbert space.
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nuclear spectral theorem, Mathematics(all), martingale, Cyclic vectors, hypercyclic and chaotic operators, generalized eigenfunction expansion, General spectral theory of ordinary differential operators, inductive spectral theorem, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators, direct integral of Hilbert spaces, Nuclear spectral theorem, Rigged Hilbert space, Martingale, Generalized eigenfunction expansion, Inductive spectral theorem, rigged Hilbert space, Direct integral of Hilbert spaces, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Vitaly system, Radon-Nikodym derivatives, spectral measures
nuclear spectral theorem, Mathematics(all), martingale, Cyclic vectors, hypercyclic and chaotic operators, generalized eigenfunction expansion, General spectral theory of ordinary differential operators, inductive spectral theorem, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators, direct integral of Hilbert spaces, Nuclear spectral theorem, Rigged Hilbert space, Martingale, Generalized eigenfunction expansion, Inductive spectral theorem, rigged Hilbert space, Direct integral of Hilbert spaces, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Vitaly system, Radon-Nikodym derivatives, spectral measures
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