Related papers: Delta Operators on Almost Symmetric Functions

We construct quantum flux operators with respect to the Poincar\'e symmetry in the massless Dirac theory at future null infinity. An anomalous helicity flux operator emerges from the commutator of the superrotation generators. The helicity…

Using vertex operator we study Macdonald symmetric functions of rectangular shapes and their connection with the q-Dyson Laurent polynomial. We find a vertex operator realization of Macdonald functions and thus give a generalized Frobenius…

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…

In this paper we study the behavior of dilation operators $ D_\lambda \colon f \mapsto f(\lambda\,\cdot) $ with $ \lambda > 1 $ in the context of Triebel-Lizorkin-Morrey spaces $\mathcal{E}^{s}_{u,p,q}(\mathbb{R}^d)$. For that purpose we…

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…

The LULU operators, well known in the nonlinear multiresolution analysis of sequences, are extended to functions defined on continuous domain, namely, a real interval $\Omega\subseteq\mathbb{R}$. Similar to their discrete counterparts, for…

We consider Toeplitz operators $T_f^{\lambda}$ with symbol $f$ acting on the standard weighted Bergman spaces over a bounded symmetric domain $\Omega\subset \mathbb{C}^n$. Here $\lambda > genus-1$ is the weight parameter. The classical…

We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.

We generalize the main theorem of Rieffel for Morita equivalence of W*-algebras to the case of unital dual operator algebras: two unital dual operator algebras A and B have completely isometric normal representations alpha, beta such that…

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…

Macdonald operators are well known as the 'commutative family' acting on the symmetric functions over Q(q,t). If we suppose that q=exp(h) and t=exp(beta h) and observe the Taylor expansion around h=0, we can see the second-degree Dunkl…

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given a positive operator $A\in\B(\h)$, and a number $\lambda\in [0,1]$, a…

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…

In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…

Inspired by J. Novak's works on the asymptotic behavior of the BGW and the HCIZ matrix integrals \cite{[N0]} and by the algebraic and geometric properties of the Hurwitz numbers \cite{[IP]}, \cite{[LZZ]}, \cite{[LR]}, \cite{[OP]},…

In the first part of this work, we consider second order supersymmetric differential operators in the semiclassical limit, including the Kramers-Fokker-Planck operator, such that the exponent of the associated Maxwellian $\phi$ is a Morse…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

Consider the family of Schr\"odinger operators (and also its Dirac version) on $\ell^2(\mathbb{Z})$ or $\ell^2(\mathbb{N})$ \[ H^W_{\omega,S}=\Delta + \lambda F(S^n\omega) + W, \quad \omega\in\Omega, \] where $S$ is a transformation on…

In this paper we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them in particular with a number of different (but equivalent) families of…

We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This…