相关论文: Weighted GJMS operators on smooth metric measure s…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…
The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover,…
In this paper we study the commutators of fractional type integral operators. This operators are given by kernels of theform $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertibles matrices and each $k_i$ satisfies a…
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called $W$-measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that ${W}$-measure is a…
We propose a definition of the weighted $\sigma_k$-curvature of a smooth metric measure space and justify it in two ways. First, we show that the weighted $\sigma_k$-curvature prescription problem is governed by a fully nonlinear second…
We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(\xi).$ With the help of counter example we also prove that the…
This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…
We present gauge invariant, self adjoint Einstein operators for mixed symmetry higher spin theories. The result applies to multi-forms, multi-symmetric forms and mixed antisymmetric and symmetric multi-forms. It also yields explicit action…
This paper is concerned with the construction of positive definite functions on a cartesian product of quasi-metric spaces using generalized Stieltjes and complete Bernstein functions. The results we prove are aligned with a…
We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of…
We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give a geometric property of the spectral geometric mean as a…
We introduce grand Morrey spaces and establish the boundedness of Hardy--Littlewood maximal, Calder\'on--Zygmund and potential operators in these spaces. In our case the operators and grand Morrey spaces are defined on quasi-metric measure…
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas of the time frequency analysis, we show that such operators are uniformly…
In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of…
We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables…
Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$ and let $w$ be a positive function on $X$ such that $w\in W^{1,s}(X,\mu)$ and $\log w\in W^{1,t}(X,\mu)$ for some $s>1$ and $t>s'$. In the…