Related papers: Nonstandard operators in Grassmannian geometry
We introduce nonabelian analogs of shift operators in the enumerative theory of quasimaps. We apply them on the one hand to strengthen the emerging analogy between enumerative geometry and the geometric theory of automorphic forms, and on…
We give an overview of the F-product construction and the corresponding nonstandard constructions for strongly continuous one-parameter semigroups of linear operators, and show that (in the case of bounded ultrapowers) both constructs are…
Let $V$ be a vector space over a field $\mathbb F$ with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If $\mathbb F=\mathbb C$, then we give canonical matrices of isometric and selfadjoint…
New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally - using…
The recently introduced by us two- and three-parameter ($p,q$)- and ($p,q,\mu$)-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum…
In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to…
We study the standard tractor bundle and the standard cotractor bundle of an almost Grassmann structure: We provide explicit formulae for their splitting operators, first BGG operators as well as prolongation connections. We characterize…
A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be…
We consider different sub-Laplacians on a sub-Riemannian manifold $M$. Namely, we compare different natural choices for such operators, and give conditions under which they coincide. One of these operators is a sub-Laplacian we constructed…
Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N=1/2…
The problem of equivalency for linear differential operators of the first order is discussed.
A new definition of canonical conformal differential operators $P_k$ ($k=1,2,...)$, with leading term a $k^{\rm th}$ power of the Laplacian, is given for conformally Einstein manifolds of any signature. These act between density bundles…
In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.
In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…
This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with H\"older continuous coefficients. The result we obtain is essentially based on parametrix method.
General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether…
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct…
This paper analyses non-regular $|2|$-graded geometries, and show that they share many of the properties of regular geometries -- the existence of a unique normal Cartan connection encoding the structure, the harmonic curvature as…