Representation of non-semibounded quadratic forms and orthogonal additivity

نویسندگان

چکیده

A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability the form, direct integral structure underlying Hilbert space and orthogonal additivity. We apply this result to several examples, including position quantum mechanics invariant under unitary separable locally compact group. case invariance group also discussed detail.

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2021

ISSN: ['0022-247X', '1096-0813']

DOI: https://doi.org/10.1016/j.jmaa.2020.124783