We consider maximal operators associated to singular averages along finite subsets Σ of the Grassmannian Gr(d,n) d-dimensional subspaces Rn. The well studied d=1 case corresponds directional function with respect arbitrary Gr(1,n)=Sn−1. provide a systematic study all cases 1≤d<n and prove essentially sharp L2(Rn) bounds for subspace averaging operator in terms cardinality Σ, no assumption on st...

Let p be a fixed prime. Throughout this paper Z, Zp, Qp, and Cp will, respectively, denote the ring of rational integers, the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, cf.[1, 2, 3]. Let vp be the normalized exponential valuation of Cp with |p| = p −vp(p) = p and let a+ pZp = {x ∈ Zp|x ≡ a( mod p N )}, where a ∈ Z lies i...

In the signal-processing literature, a frame is mechanism for performing analysis and reconstruction in Hilbert space. By contrast, quantum theory, positive operator-valued measure (POVM) decomposes Hilbert-space vector purpose of computing measurement probabilities. Frames their most common generalizations can be seen to give rise POVMs, but does every reasonable POVM arise from type frame? We...

Abstract It is proved that each Gaussian cocycle over a mildly mixing transformation either coboundary or sharply weak mixing. The class of non-singular infinite direct products T transformations $T_n$ , $n\in \mathbb N$ finite type studied. shown if mixing, the sequence Radon–Nikodym derivatives asymptotically translation quasi-invariant and conservative then Maharam extension This technique p...