We prove that the $L_4$ norm of vertical perimeter any measurable subset $3$-dimensional Heisenberg group $\mathbb{H}$ is at most a universal constant multiple (Heisenberg) subset. show this isoperimetric-type inequality optimal in sense there are sets for which it fails to hold with replaced by $L_q$ $q<4$. This contrast $5$-dimensional setting, where above result holds $L_2$ norm. The proof...

Let (,) be a measurable space with -finite continuous measure, ()=. A linear operator T:L1()+L()L1()+L() is called the Dunford-Schwartz if ||T(f)||1||f||1 (respectively, ||T(f)||||f||) for all fL1() fL()). {Tt}t0is strongly in L1() semigroup of operators, then each At(f)=1t∫0tTs(f)ds∈L1(Ω){{{A_t(f)} ={\frac{1}{t}} {\int_0^t} {T_s(f)} ds \in L_1(\Omega)}} has unique extension to operator, which ...

A Bernoulli Gibbsian line ensemble $\mathfrak{L} = (L_1, \dots, L_N)$ is the law of trajectories $N-1$ independent random walkers $L_1, L_{N-1}$ with possibly initial and terminal locations that are conditioned to never cross each other or a given up-right path $L_N$ (i.e. $L_1 \geq \cdots L_N$). In this paper we investigate asymptotic behavior sequences ensembles $\mathfrak{L}^N (L^N_1, L^N_N)...

A closer and more detailed study of neutrino oscillation, in addition to assisting us founding physics beyond the standard model, can potentially be used understand fundamental aspects quantum mechanics. In particular, we know that oscillation occurs because states produced detected neutrinos are a coherent superposition mass eigenstates, this coherency is maintained during propagation due smal...

We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ differential operators $L_1$ $L_{2}$, that has implications for spectral properties of $K$. This work complements our explicit characterization commuting pairs $KL=LK$ provides an exhaustive list kernels admitting or sesquicommuting operators.

Abstract Gibbs ringing is a feature of MR images caused by the finite sampling acquisition space ( k -space). It manifests itself with patterns around sharp edges which become increasingly significant for low-resolution acquisitions. In this paper, we model artefact removal as constrained variational problem where data discrepancy, represented in denoising and convolutive form, balanced to spar...