Complex-valued valuations on Lp spaces
Lijuan Liu
TL;DR
This paper classifies all continuous complex-valued valuations on Lebesgue measurable functions that are invariant under translation and rotation, providing a comprehensive understanding of their structure.
Contribution
It offers a complete classification of continuous translation and rotation invariant complex-valued valuations on Lebesgue and spherical Lebesgue functions, respectively.
Findings
Complete classification of translation invariant valuations.
Complete classification of rotation invariant valuations.
Provides foundational results for complex-valued valuations.
Abstract
All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified. And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurable functions are also completely classified.
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Taxonomy
TopicsAdvanced Banach Space Theory · Mathematical Dynamics and Fractals · Functional Equations Stability Results