Related papers: When is the operation $\tau_{T,L}$ a triangle func…

For a compact, irreducible, $\partial$-irreducible, an-annular bounded 3-manifold $M\ne\mathbb{B}^3$, then any triangulation $\mathcal{T}$ of $M$ can be modified to an ideal triangulation $\mathcal{T}^*$ of $\stackrel{\circ}{M}$. We use the…

Let $\mathfrak{M}$ be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace $\tau$. A closed densely defined operator $x$ affiliated with $\mathfrak{M}$ is called $\tau$-measurable if there…

We consider the class of positive bounded and semi-continuous functions defined on the two dimensional torus If f belongs to this class, then f will be considered as the symbol of a Toeplitz operator truncated on a triangle parametrised by…

We introduce multilinear operators, that generalize Hirota's bilinear $D$ operator, based on the principle of gauge invariance of the $\tau$ functions. We show that these operators can be constructed systematically using the bilinear $D$'s…

The theory of slice regular functions of a quaternionic variable extends the notion of holomorphic function to the quaternionic setting. This theory, already rich of results, is sometimes surprisingly different from the theory of…

We study an elliptic operator $L:=\mathrm{div}(A\nabla \cdot)$ on the upper half plane $\mathbb{R}^2_+$. There are several conditions on the behavior of the matrix $A$ in the transversal $t$-direction that yield $\omega\in…

Let $\mathcal{D}$ be the classical Dirichlet space, the Hilbert space of holomorphic functions on the disk. Given a holomorphic symbol function $b$ we define the associated Hankel type bilinear form, initially for polynomials f and g, by…

A classical result of Sz.-Nagy asserts that a Hilbert-space contraction operator $T$ can be lifted to an isometry $V$. A more general multivariable setting of recent interest for these ideas is the case where (i) the unit disk is replaced…

Generalized Toeplitz plus Hankel operators $T(a)+H_{\alpha}(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\alpha$ changing the orientation of the unit circle $\mathbb{T}$ are considered on the Hardy spaces…

We derive two main results: First, assume that $A$, $B$, $A_n$, $B_n$ are self-adjoint operators in the Hilbert space $\mathcal{H}$, and suppose that $A_n$ converges to $A$ and $B_n$ to $B$ in strong resolvent sense as $n \to \infty$. Fix…

We consider the $2m$-th order elliptic boundary value problem $Lu=f(x,u)$ on a bounded smooth domain $\Omega\subset\R^N$ with Dirichlet boundary conditions on $\partial\Omega$. The operator $L$ is a uniformly elliptic linear operator of…

A linear operator $T$ between two lattice-normed locally solid Riesz spaces is said to be $p_\tau$-continuous if, for any $p_\tau$-null net $(x_\alpha)$, the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is also said to be $p_\tau$-bounded…

Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is…

Let a function $F: [0,1]^2\rightarrow [0,1]$ be given by $F(x,y)= f^{(-1)}(T(f(x), f(y)))$ where $f :[0,1]\rightarrow [0,1]$ is a monotone function, $f^{(-1)}$ is the pseudo-inverse of $f$ and $T$ is a triangular norm. This article…

We study an elliptic operator $L:=\mathrm{div}(A\nabla \cdot)$ on the upper half space. It is known that solvability of the Regularity problem in $\dot{W}^{1,p}$ implies solvability of the adjoint Dirichlet problem in $L^{p'}$. Previously,…

A continuous linear operator $T:E \to F$ is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon…

If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…

We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…

We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…

In this paper we consider $L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons. In particular, assume that $(M,g)$ is a gradient shrinking or steady K\"ahler-Ricci soliton, then we prove that any pluriharmonic…