A Certain p-Adic Spectral Theorem

有界性及某类p进Hardy-Littlewood-Pólya型算子的范数

Boundedness and norm of certain p-adic Hardy-Littlewood-Pólya-type operators

本文研究了p进Hardy-Littlewood-Pólya型算子的有界性和范数，通过参数引入，刻画了其在p进加权Lebesgue空间上的L^q-L^r有界性并给出了特殊情形下的精确范数估计。

On a characterisation theorem for $a$-adic solenoids

According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given another. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an $a$-adic solenoid $Σ_a$ without elements of order 2, assuming that the characteristic functions of the random variables do not vanish, and coefficients of the linear forms are topological automorphisms of $Σ_a$.

Analytic van der Corput Lemma for p-adic and F_q((t)) oscillatory integrals, singular Fourier transforms, and restriction theorems

We give the p-adic and F_q((t)) analogue of the real van der Corput Lemma, where the real condition of sufficient smoothness for the phase is replaced by the condition that the phase is a convergent power series. This van der Corput style result allows us, in analogy to the real situation, to study singular Fourier transforms on suitably curved (analytic) manifolds and opens the way for further applications. As one such further application we give the restriction theorem for Fourier transforms of L^p functions to suitably curved analytic manifolds over non-archimedean local fields, similar to …