Dyadic spike blocks yield counterexamples where lacunary averages diverge to infinity a.e. for mean-zero functions in all L^q and for L^p functions, resolving Erdős problems #995 and #996 negatively.
On the cross-norm of the direct product ofC ∗-algebras.Tohoku Math
7 Pith papers cite this work. Polarity classification is still indexing.
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Synchrotron polarization at the black hole horizon follows a universal pattern set solely by spin and inclination.
Introduces Higgs bundles on the Fargues-Fontaine curve, establishes a BNR correspondence, and shows an injective étale-stack map from B_dR^+-affine Springer fibers to the Hitchin fiber inducing category equivalence on geometric points.
Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
Establishes boundedness for the regularized bilinear cone multiplier on R^2 x R^2 via square function decomposition, maximal function estimates, and geometric methods from Córdoba and Carbery.
Reduced cross-sectional algebra of an approximation-property Fell bundle over an inverse semigroup is exact iff its unit fiber is exact.
The thesis compiles work on graph bandits (spectral smoothness, side observations, influence maximization) and structured bandits (kernel, polymatroid, function optimization with unknown smoothness, infinite arms) to improve practicality.
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Exactness and Fell bundles with the approximation property over inverse semigroups
Reduced cross-sectional algebra of an approximation-property Fell bundle over an inverse semigroup is exact iff its unit fiber is exact.