ﻻ يوجد ملخص باللغة العربية
A Borel probability measure $mu$ on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of the Hilbert space $L^2(mu)$. In this paper, we characterize all spectral measures in the field $mathbb{Q}_p$ of $p$-adic numbers.
In this paper we prove that if ${varphi_i(x)=lambda x+t_i}$ is an equicontractive iterated function system and $b$ is a positive integer satisfying $frac{log b}{log |lambda|} otinmathbb{Q},$ then almost every $x$ is normal in base $b$ for any non-atomic self-similar measure of ${varphi_i}$.
We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating a MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all suc
We prove a $p$-adic version of the Integral Geometry Formula for averaging the intersection of two $p$-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective set (repr
We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian, and to the boundedness of $L^p$ norms of eigenfunctions of the Laplacian. We formulate a conjecture, and partially prove it.
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the $p$-frame energies, i.e. energies with the kernel given by the absolute value of the inner product rai