Related papers: Differentiability of Lipschitz Functions in Lebesg…
The Linnik phenomenon concerning the repelling effect of Siegel's zeros is extended to L-functions in a family wider than hitherto considered.
We construct a real sequence $\{\lambda_n\}_{n=1}^{\infty}$ satisfying $\lambda_n = n + o(1)$, and a Schwartz function $f$ on $\mathbb{R}$, such that for any $N$ the system of translates $\{f(x - \lambda_n)\}$, $n > N$, is complete in the…
We give sufficient geometric conditions, not involving capacities, for a compact null set to be removable for the Sobolev functions on weighted $\mathbb R^n$, defined as the closure of smooth functions in the weighted Sobolev norm. Our…
We characterize all (absolute) 1-Lipschitz retracts Q of R^n with the maximum norm. Omitting two technical details, they coincide with the subsets written as the solution set of (at most) 2n inequalities like follows. For every coordinate…
We show that the set of Misiurewicz maps has Lebesgue measure zero in the space of rational functions for any fixed degree greater than or equal to 2 (generalising the earlier version math.DS/0701382).
The Dirichlet--Hardy space $\Ht$ consists of those Dirichlet series $\sum_n a_n n^{-s}$ for which $\sum_n |a_n|^2<\infty$. It is shown that the Blaschke condition in the half-plane $\operatorname{Re} s>1/2$ is a necessary and sufficient…
We prove that a functional with Lipschitzian derivative, when restricted to suitable spheres centered at a noncritical point, has a unique maximum.
In this article we obtain an "off-diagonal" version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12]…
We look at a measure, $\lambda^\infty$, on the infinite-dimensional space, ${\mathbb R}^\infty$, for which we attempt to put forth an analogue of the Lebesgue density theorem. Although this measure allows us to find partial results, for…
We prove that for a given Banach space $X$, the subset of norm attaining Lipschitz functionals in $\mathrm{Lip}_0(X)$ is weakly dense but not strongly dense. Then we introduce a weaker concept of directional norm attainment and demonstrate…
In this paper, some existence results for sign-changing critical points of locally Lipschitz functionals in real Banach space are obtained by the method combining the invariant sets of descending ow method with a quantitative deformation.…
In this paper a special class of local zeta functions is studied. The main theorem states that the functions have all zeros on the line Re (s)=1/2. This is a natural generalization of the result of Bump and Ng stating that the zeros of the…
This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of…
We give a new approach to the infinitesimal structure of Lipschitz maps into L^1. As a first application, we give an alternative proof of the main theorem from an earlier paper, that the Heisenberg group does not admit a bi-Lipschitz…
We give sufficient conditions for a metric space to bilipschitz embed in L_1. In particular, if X is a length space and there is a Lipschitz map u:X--->R such that for every interval I in R, the connected components of the inverse image…
There exist small perturbations of L-functions, satisfying the appropriate functional equation, for which the analogue of the Riemann hypothesis fails radically. Moreover, this phenomenon is generic. However, there also exist small…
We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could…
A Steinhaus set $S \subseteq \RR^d$ for a set $A \subseteq \RR^d$ is a set such that $S$ has exactly one point in common with $\tau A$, for every rigid motion $\tau$ of $\RR^d$. We show here that if $A$ is a finite set of at least two…
On a convex bounded open set, we prove that Poincar\'e-Sobolev constants for functions vanishing at the boundary can be bounded from below in terms of the norm of the distance function in a suitable Lebesgue space. This generalizes a result…
In a series of papers, M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the…