Bounded $q$-variation Functions in Spaces with Indefinite Metric
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i2.5565Keywords:
Krein space, fundamental symmetry, q-variation, total q-variation, bounded q-variation, q-normAbstract
In this paper we establish the definition of bounded q-variation functions on Krein spaces (definition 7) and give a complete characterisation by comparing it with bounded q-variation functions on classical Hilbert spaces and with Hilbert spaces associated to a Krein space (theorem 6). The fundamental tools of the theory of bounded q-variation functions in the formalism of Krein spaces are described (theorems 7, 8). Furthermore, we endow the spaces of bounded q-variation functions in Krein spaces with a norm, which we have called q-norm (theorem 13).
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Copyright (c) 2025 Osmin Ferrer Villa, Jos´e Naranjo Mart´ınez
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