Related papers: $L^p$ Expander Graphs

We discuss $\mathrm{L}^p$ fiber spaces which appear, e.g., as extrapolation spaces of unbounded multiplication operators which in turn are motivated, for instance, by non-autonomous evolution equations.

We provide upper bounds on the $L(p,q)$-labeling number of graphs which have interval (or circular-arc) representations via simple greedy algorithms. We prove that there exists an $L(p,q)$-labeling with span at most…

We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^p$-norm can be upper bounded, up to an asymptotically small error, by the operator norm of the same polynomial evaluated in free…

We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator $S$ obtained by restricting the self-adjoint operator $A:\D(A)\subseteq\H\to\H$ to the dense, closed with respect…

We give a delocalization estimate for eigenfunctions of the discrete Laplacian on large $d+1$-regular graphs, showing that any subset of the graph supporting $\epsilon$ of the $L^2$ mass of an eigenfunction must be large. For graphs…

Considering a graph $H$ of order $p$, a generalized $H$-join operation of a family of graphs $G_1,..., G_p$, constrained by a family of vertex subsets $S_i \subseteq V(G_i)$, $i=1,..., p,$ is introduced. When each vertex subset $S_i$ is…

Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$. Uniform asymptotic expansions of the corresponding empirical eigenvalues and…

Peral/Miyachi's celebrated theorem on fixed time $L^{p}$ estimates with loss of derivatives for the wave equation states that the operator $(I-\Delta)^{- \frac{\alpha}{2}}\exp(i \sqrt{-\Delta})$ is bounded on $L^{p}(\mathbb{R}^{d})$ if and…

For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are…

In this work, we relate girth and path-degeneracy in classes with sub-exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor-closed classes that are tight up to a constant factor (and tight up to…

We establish local $(L^p,L^q)$ mapping properties for averages on curves. The exponents are sharp except for endpoints.

We introduce and develop a theory of limits for sequences of sparse graphs based on $L^p$ graphons, which generalizes both the existing $L^\infty$ theory of dense graph limits and its extension by Bollob\'as and Riordan to sparse graphs…

A convolution operator in $\mathbb{R}^d$ with kernel in $L_q$ acts from $L_p$ to $L_s$, where $1/p+1/q=1+1/s$. The main theorem states that if $1<q,p,s<\infty$, then there exists an $L_p$ function of unit norm on which the $s$-norm of the…

Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…

In this paper we study the $L^p-L^r$ boundedness of the extension operators associated with paraboloids in vector spaces over finite fields.In higher even dimensions, we estimate the number of additive quadruples in the subset $E$ of the…

We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving…

We study an asymptotic behavior of the probabilities of first-order properties of random graph G(N,p) in the article. We conider p such that lnp=-alnN, a>0. We find values of parameter a from (1-exp(ln2(1-k)),1) such that the random graph…

We study the equivalence between the $L^p$-parabolicity, the $L^q$-Liouville property of positive super-harmonic functions, and the existence of nonharmonic positive solutions to the following elliptic differential system \begin{equation*}…

We precisely evaluate the operator norm of the uncentered Hardy-Littlewood maximal function on $L^p(\Bbb R^1)$. We also compute the operator norm of the uncentered Hardy-Littlewood maximal function over rectangles on $L^p(\Bbb R^n)$, and we…

We investigate $L^p$ boundedness of the maximal function defined by the averaging operator $f\to \mathcal{A}_t^s f$ over the two-parameter family of tori $\mathbb{T}_t^{s}:=\{ ( (t+s\cos\theta)\cos\phi,\,(t+s\cos\theta)\sin\phi,\,…