Related papers: Classe d'equivalence Formelle D'un D-Module D'Airy
Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8.
A differential-algebraic geometric analogue of the Dixmier-Moeglin equivalence is articulated, and proven to hold for $D$-groups over the constants. The model theory of differentially closed fields of characteristic zero, in particular the…
Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…
We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for…
Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There…
We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with…
In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and study certain operators generalizing the classical umbral…
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
If $\fg$ is a semisimple Lie algebra, we describe the prime factors of $\mcU(\fg)$ that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also…
This paper introduces an approach to validate the functional equivalence of planning domain models. Validating the functional equivalence of planning domain models is the problem of formally confirming that two planning domain models can be…
We construct a cofibrantly generated model structure on the category of differential non-negatively graded quasi-coherent commutative $D_X$-algebras, where $D_X$ is the sheaf of differential operators of a smooth afine algebraic variety X.…
The Airy transform is an ideally suited tool to treat problem in classical and quantum optics. Even though the relevant mathematical aspects have been thoroughly investigated, the possibility it offers are wide and some aspects, as the link…
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…
Let G be a profinite group which is topologically finitely generated, p a prime number and d an integer. We show that the functor from rigid analytic spaces over Q_p to sets, which associates to a rigid space Y the set of continuous…
The study of Cowen-Douglas operators not only involves traditional operator-theoretic tools but also concepts and results from complex geometry on holomorphic vector bundles. We make use of the ratio of the metric matrices first considered…
We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…
The moduli space M(r,d) of stable, rank r, degree d vector bundles on a smooth projective curve of genus g>1 is shown to be birational to M(h,0) x A, where h=hcf(r,d) and A is affine space of dimension (r^2-h^2)(g-1). The birational…
In this paper we make an initial study on type D moduli spaces in positive characteristic $p\neq 2$, where we allow $p$ ramified in the definite quaternion algebra. We classify the isogeny classes of $p$-divisible groups with additional…
Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang-Hilbert-type integral inequalities with the best constant factors. Equivalent forms, the…
We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the extraction of (formal) Taylor coefficients using a residue…