Complete Sobolev Type Inequalities
Haojian Li

TL;DR
This paper extends Sobolev inequalities to noncommutative quantum settings, generalizing classical inequalities using monotone metrics and exploring applications in quantum models.
Contribution
It introduces a framework for Sobolev inequalities in noncommutative spaces, broadening their applicability to quantum information theory.
Findings
Generalized monotone metrics in quantum state spaces
Established Sobolev inequalities in noncommutative contexts
Applied results to quantum models like random transpositions
Abstract
We establish Sobolev type inequalities in the noncommutative settings by generalizing monotone metrics in the space of quantum states, such as matrix-valued Beckner inequalities. We also discuss examples such as random transpositions and Bernoulli-Laplace models.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Fatigue and fracture mechanics · Numerical methods in inverse problems
