Search

This paper is devoted to the study of the restriction problem in harmonic analysis. Based on the spherical harmonics expansion and analyzing the asymptotic behavior of the Bessel function, we show that a modified linear adjoint restriction estimate holds for all Schwartz functions compactly supported on the cone, which generalizes Shao's result. [ABSTRACT FROM AUTHOR]

We show that a holomorphic mapping sending one generic submanifold into another of the same dimension is CR transversal to the target submanifold provided that the source manifold is of finite type and the map is of generic full rank. This result and its corollaries completely resolve two questions posed by Linda P. Rothschild and the first author in 2006. Another one of our main results, in the special setting of hypersurfaces, was also explicitly stated as a conjecture by B. Lamel and N. Mir in a paper from 2006. [ABSTRACT FROM AUTHOR]

The holomorphy conjecture predicts that the topological zeta function associated to a polynomial $ f \in \mathbb{C}[x_1,\ldots,x_n]$ is holomorphic unless $ d$. In this paper, we generalise the holomorphy conjecture to the setting of arbitrary ideals in $ \mathbb{C}[x_1,\ldots,x_n]$. [ABSTRACT FROM AUTHOR]

Recently Alonso, Martín and Papini conjectured that the value of the von Neumann-Jordan constant is less than or equal to that of the James constant. This paper presents an affirmative answer to such a conjecture. Moreover, we obtain a sharp estimate for the von Neumann-Jordan constant. [ABSTRACT FROM AUTHOR]

In this paper, we prove that separable subgroups have bounded packing in ambient groups. The notion bounded packing was introduced by Hruska and Wise, and, in particular, our result confirms a conjecture of theirs which states that each subgroup of a virtually polycyclic group has the bounded packing property. [ABSTRACT FROM AUTHOR]