A discrete Gibbsian line ensemble $\mathfrak{L} = (L_1,\dots,L_N)$ consists of $N$ independent random walks on the integers conditioned not to cross one another, i.e., $L_1 \geq \cdots L_N$. In this paper we provide sufficient conditions for convergence a sequence suitably scaled ensembles $f^N (f_1^N,\dots,f_N^N)$ as number curves tends infinity. Assuming log-concavity and KMT-type coupling wa...

We generalize the classical Lebesgue's theorem to multi-dimensional functions. prove that Cesàro means of Fourier series function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge $f$ at each strong Lebesgue point.

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

Given a perfect coloring of graph, we prove that the $L_1$ distance between two rows adjacency matrix graph is not less than corresponding parameter coloring. With help an algebraic approach, deduce corollaries this result for $2$-colorings, colorings in distance-$l$ graphs and distance-regular graphs. We also provide examples when obtained property reject several putative matrices infinite

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...