We prove that the maximal functions associated with a Zygmund dilation dyadic structure in three-dimensional Euclidean space, and flag two-dimensional cannot be bounded by multiparameter sparse operators corresponding grid. also obtain supplementary results about absence of domination for strong function.

Following the same steps made for a scalar field in parallel publication, we propose class of perturbative theories quantum gravity based on fractional operators, where kinetic operator graviton is either derivatives or covariant d'Alembertian. The classical action each theory constructed and equations motion are derived. Unitarity renormalizability with d'Alembertian also considered. We argue ...

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

We obtain uniform non-semiclassical spectral inequalities for Schrödinger operators with increasing electric potentials.

A classical result in metric geometry asserts that any n-point metric admits a linear-size spanner of dilation O(log n) [PS89]. More generally, for any c > 1, any metric space admits a spanner of size O(n), and dilation at most c. This bound is tight assuming the well-known girth conjecture of Erdős [Erd63]. We show that for a metric induced by a set of n points in high-dimensional Euclidean sp...

In the Hilbert space ?2 ?(Z; E) (Z := {0,? 1, ? 2, ...}, dim E = N < ?), maximal dissipative singular second-order matrix difference operators that extensions of a minimal symmetric operator with deficiency indices (2N, 2N) (in limit-circle cases at ?) are considered. The general boundary conditions investigated. For operator, self-adjoint dilation and is its incoming outgoing spectral repre...