Related papers: On infinite matrices, Schur products, and operator…

This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…

We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions) where this problem can be posed precisely. We consider…

If $\,\mu \,$ is a finite positive Borel measure on the interval $\,[0,1)$, we let $\,\mathcal H_\mu \,$ be the Hankel matrix $\,(\mu _{n, k})_{n,k\ge 0}\,$ with entries $\,\mu _{n, k}=\mu _{n+k}$, where, for $\,n\,=\,0, 1, 2, \dots $,…

We establish connections between Schur parameters of the Schur class operator-valued functions, the corresponding simple conservative realizations, lower triangular Toeplitz matrices, and Kre\u\i n shorted operators. By means of Schur…

We construct strongly mixing invariant measures with full support for operators on F-spaces which satisfy the Frequent Hypercyclicity Criterion. For unilateral backward shifts on sequence spaces, a slight modification shows that one can…

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu}=(\mu_{n,k})_{n,k\geq 0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_{n}=\int_{[0,1)}t^nd\mu(t)$, induces formally the operator as…

The main questions raised in this paper are to find the sufficient conditions that make multi-sublinear operators $T$ and their commutators ${T_{\prod \vec b }}$, ${T_{\sum {\vec b} }}$ to be bounded on three kinds of generalized weighted…

We construct examples of one-dimensional Schr\"odinger operators that illustrate the subtle nature of fractal continuity properties of spectral measures. First, we present half-line operators whose spectral measures have packing dimension…

Kuelbs-Steadman spaces are introduced in this article on a separable metric space with finite diameter and finite positive Borel measure. Kuelbs-Steadman spaces of the Lipschitz type are also discussed. Various inclusion properties are also…

The extended semantic realism (ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as…

We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…

The purpose of this paper is threefold. First the natural extension of Riesz potentials to the context of quasi metric measure spaces for the class of upper doubling measures are studied on Lebesgue spaces, obtaining necessary and…

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse…

Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and <, >_A : H \times H \to C the bounded sesquilinear form induced by a selfadjoint A in L(H), < \xi, \eta >_A = < A \xi, \eta >, \xi, \eta in H. Given T in…

We extend the study of \emph{melonic} quartic tensor models to models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and iterated…

Let $(\cx,\,d,\,\mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors show that for the maximal Calder\'on-Zygmund operator associated with a…

We introduce the concept of a \mu-scale invariant operator with respect to unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is \mu-scale invariant for some \mu >0,…

We study the quasi-nilpotency of generalized Volterra operators on spaces of power series with Taylor coefficients in weighted $\ell^p$ spaces $1<p<+\infty$ . Our main result is that when an analytic symbol $g$ is a multiplier for a…