Related papers: Mourre theory for analytically fibered operators r…
In this note a characterization of anallytically Riesz operators is given. This work completes the article [1].
Via the new weight $A_{\vec p}^{\infty}(\varphi)$ and the new $BMO$ function, the authors introduce a new class of multilinear square operators $T$ with generalized kernels. The boundedness of multilinear commutators and multilinear…
We construct a general theory of operator monotonicity and apply it to the Fr\"ohlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Fr\"ohlich model.
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate…
For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…
A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a…
For two positive definite adjointable operators $M$ and $N$, and an adjointable operator $A$ acting on a Hilbert $C^*$-module, some properties of the weighted Moore-Penrose inverse $A^\dag_{MN}$ are established. When $A=(A_{ij})$ is…
The field of C*-algebras over the interval [0,2] for which the fibers are the Soft Tori is shown to be continuous. This result is applied to show that any pair of non-commuting unitary operators can be perturbed (in a weak sense) in such a…
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory generalizes the tensor category theory for…
Rota-Baxter operators, $\mathcal{O}$-operators on Lie algebras and their interconnected pre-Lie and post-Lie algebras are important algebraic structures with applications in mathematical physics. This paper introduces the notions of a…
We discuss a general framework for the analytic Langlands correspondence over an arbitrary local field F introduced and studied in our works arXiv:1908.09677, arXiv:2103.01509 and arXiv:2106.05243, in particular including non-split and…
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…
We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we…
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…
We give a new construction of functors from the category of modules for the associative algebras $A_n(V)$ and $A_g(V)$ associated with a vertex operator algebra $V$, defined by Dong, Li and Mason, to the category of admissible $V$-modules…
The operator monotone functions defined in the positive half-line are of particular importance. We give a version of the theory in which integral representations for these functions can be established directly without invoking L\"owner's…
We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2-cofiniteness. We also showed that the tensor product theory develops…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…