Related papers: The Penrose Transform for Complex Projective Space

In this text, we explore the tools that Projective Differential Geometry can provide for the asymptotic analysis of classical fields on projectively compact manifolds. We emphasise on the case of order 2-compactifications and develop, in…

We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…

For a projective hypersurface $X \subset \P^n$, the images of the polar maps of degree $k$ are studied. The cohomology class defined by these maps is calculated and classical results on dual varieties are presented as applications.

We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.

Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…

We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex…

We construct explicit generators of the K-theory and K-homology of the coordinate algebra of `functions' on quantum projective spaces. We also sketch a construction of unbounded Fredholm modules, that is to say Dirac-like operators and…

Let $M$ be either a projective manifold $(M,Pi)$ or a pseudo-Riemannian manifold $(M,g).$ We extend, intrinsically, the projective/conformal Schwarzian derivatives that we have introduced recently, to the space of differential operators…

This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…

This is the first paper in a series of two papers. In this paper we construct complexes of invariant differential operators which live on homogeneous spaces of $|2|$-graded parabolic geometries of some particular type. We call them…

In this paper we derive a simple and useful combinatorial formula for the push-forwards of cohomology classes down projective towers, in terms of the push-forwards down the individual steps in the tower.

The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition…

In this paper, new block representations of Moore-Penrose inverses for arbitrary complex $2\times2$ block matrices are given. The approach is based on block representations of orthogonal projection matrices.

Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson…

Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures…

We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a delicate interplay between integral, rational, and mod p…

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…

This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…

For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the…

We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…