Related papers: Factorization of Laplace operators on higher spin …
Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…
The Dirac equation is considered in the background of potentials of several types, namely scalar and vector-potentials as well as "Dirac-oscillator" potential or some of its generalisations. We investigate the radial Dirac equation within a…
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…
We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order…
In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater…
We consider fermionic fields of higher spin on a four-dimensional de Sitter background. A particular emphasis is placed on the Rarita-Schwinger spin-$\tfrac{3}{2}$ case. Both massive fields and gauge fields are considered, and their…
A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…
We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these…
Quadratic Wiener functionals are investigated systematically through transformations of order one on the Wiener space with the help of Malliavin calculus. The bi-directional relationship between quadratic Wiener functionals and…
We investigate the various types of weight raising and weight lowering operators on quasi-modular forms, or equivalently on Shimura's vector-valued modular forms involving symmetric power representations. We also present all the…
We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\alpha and to the proper equations of motion for the components, i.e. the Maxwell…
We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we…
In this paper we characterize the closed invariant subspaces for the ($*$-)multiplier operator of the quaternionic space of slice $L^2$ functions. As a consequence, we obtain the inner-outer factorization theorem for the quaternionic Hardy…
In [M. R\"osler and M. Voit. Integral Representation and Uniform Limits for Some Heckman-Opdam Hypergeometric Functions of type BC, Transactions of the American Mathematical Society, Vol. 368, No. 8, 6005-6032, 2016.], R\"osler and Voit…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
In this article we show that the fractional Laplacian in $R^{2}$ can be factored into a product of the divergence operator, a Riesz potential operator, and the gradient operator. Using this factored form we introduce a generalization of the…
Let $X$ be a metric space with a doubling measure. Let $L$ be a nonnegative self-adjoint operator acting on $L^2(X)$, hence $L$ generates an analytic semigroup $e^{-tL}$. Assume that the kernels $p_t(x,y)$ of $e^{-tL}$ satisfy Gaussian…
This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume…
Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential…
We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one…