Related papers: On Some Conformally Invariant Operators in Euclide…
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
In this paper, we study the conformally invariant field equations for vector-spinor field in de Sitter space-time. The solutions are also obtained in terms of the de Sitter-Dirac plane waves. The related two-point functions are calculated…
We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($d\geqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the…
In this paper we show variant of the spectral theorem using an algebraic Jordan-Schwinger map. The advantage of this approach is that we don't have restriction of normality on the class of operators we consider. On the other side, we have…
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are…
We give a classification of $1^{st}$ order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so called metaplectic contact projective type. These bundles are associated via…
The problems considered in this paper come as a natural continuation of our program to develop a free analogue of Sz.-Nagy-Foias theory, for row contractions. The paper is structured as follows: Introduction Part I. Unitary invariants for…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
We develop theory and software for rotation equivariant operators on scalar and vector fields, with diverse applications in simulation, optimization and machine learning. Rotation equivariance (covariance) means all fields in the system…
The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of…
Twistor correspondences for R-invariant indefinite self-dual conformal structures on R^4 are established explicitly. These correspondences are written down by using a natural integral transform from functions on a two dimensional cylinder…
These notes are based on my lectures given at $\text{ST}^4$ 2025 held at IISER Bhopal. We study the application of spinor and twistor methods to three dimensional conformal field theories in these notes. They are divided into three parts…
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…