Related papers: Green equivalences in equivariant mathematics
We establish a general relation between the statistics of the local Green's function for systems with chaotic wave scattering and a uniform energy loss (absorption) and its two-point correlation function for the same system without…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…
We develop the theory of ind-geometric stacks, in particular their coherent and ind-coherent sheaf theory. This provides a convenient framework for working with equivariant sheaves on ind-schemes, especially in derived settings. Motivating…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
We consider the two-dimensional non-relativistic Coulomb problem with the aid of the momentum space construction of the associated Green's function. Our presentation has precursors in three dimensions. It is mainly Schwinger's approach…
A duality of $\kappa$-normed topological vector spaces is defined and investigated. For such spaces the analog of the Mackey-Arens theorem is proved. There are investigated cases, when $\kappa$-normability of a topological vector space…
We introduce {\em Green fields}, as commutative Green biset functors with no non-trivial ideals. We state some of their properties and give examples of known Green biset functors which are Green fields. Among the properties, we prove some…
This work deals with the obtaining of solutions of first and second order Stieltjes differential equations. We define the notions of Stieltjes derivative on the whole domain of the functions involved, provide a notion of n-times…
We prove that a pair of singularities related by a transformation arising from the McKay correspondence are orbifold equivalent. From this we deduce a new proof of a McKay type equivalence for the matrix factorization categories.
Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put…
We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same for…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…
We give a homotopy theoretic characterization of stacks on a site $\cC$ as the {\it homotopy sheaves} of groupoids on $\cC$. We use this characterization to construct a model category in which stacks are the fibrant objects. We compare…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.
We describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.
For any discrete group $\Gamma$ and any 2-dimensional complex representation $\rho$ of $\Gamma$, we introduce the notion of $\rho-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also…