Related papers: Penrose transform and monogenic functions
The theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincar\'e…
We construct an explicit de Rham isomorphism relating the cohomology rings of Banagl's de Rham and spatial approach to intersection space cohomology for stratified pseudomanifolds with isolated singularities. Intersection space…
Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are…
Viewing a fan as a partially ordered set (of cones) we consider a category of sheaves on the fan which corresponds to a category of equivariant sheaves on the corresponding toric variety if the fan is rational. In this category we define an…
The isomorphism between the reduction algebra and the invariant differential operators on G/H is sketched.
In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
In this paper, we address the integration problem of the isomonodromic system of quantum differential equations ($qDE$s) associated with the quantum cohomology of $\mathbb P^1$-bundles on Fano varieties. It is shown that bases of solutions…
We diagonalize the transfer matrix of the inhomogeneous vertex models of the 6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex operators. The special cases of those models were used to diagonalize the s-d…
We establish some properties of the derived category of torus-equivariant coherent sheaves on a split toric stack bundle. Our main result is a semi-orthogonal decomposition of such a category.
Weighted V-line transforms map a symmetric tensor field of order $m\ge0$ to a linear combination of certain integrals of those fields along two rays emanating from the same vertex. A significant focus of current research in integral…
On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
Distributional tensor fields can be regarded as multilinear mappings with distributional values or as (classical) tensor fields with distributional coefficients. We show that the corresponding isomorphisms hold also in the bornological…
Spencer cohomology theory studies the cohomology of chain complexes of modules over the ring of differential operators $\mathscr{D}$ of a smooth analytic space. In this paper we give a generalisation of Spencer cohomology suitable for…
The Fourier transform and its inverse are well-known to have complex conjugate integral kernels. S.~Saitoh demonstrated that this relationship extends to the theory of integral transforms of Hilbert spaces of functions under certain…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
We characterize the condition $(\Omega)$ for smooth kernels of partial differential operators in terms of the existence of shifted fundamental solutions satisfying certain properties. The conditions $(P\Omega)$ and…
The analysis of branching problems for restriction of representations brings the concept of symmetry breaking transform and holographic transform. Symmetry breaking operators decrease the number of variables in geometric models, whereas…