Related papers: Green's function for certain domains in the Heisen…
We prove that Lipschitz intrinsic graphs in the Heisenberg groups $H^n$, with $n>1$, which are vanishing viscosity solutions of the minimal surface equation are smooth.
We study Sp(2n,R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL(2n,R). For even n we give expressions for such invariant functionals using an explicit realization of the space of smooth vectors in the…
In the paper we find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the…
Closed expression for the Green's function of the stationary two-dimensional Schrodinger equation for an electron in group-VI dichalcogenides in the presence of a magnetic field is obtained in terms of the Whittaker functions. The resulting…
In this work, the Heun operator is written as an element in the universal enveloping algebra of the Lie algebra $\mathscr{G}=\mathscr{L}(G)$ of the Lie group $G=SL(2,\mathbb{C})$. The Green function and the spectral shift function of the…
The Green's function of the discrete Sch\"odinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting appropriate potentials. We show two ways of the expression for the Green's…
Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
Let G/H be a hyperbolic space over R C or H, and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any…
A characterization of maximal domains of existence of adapted complex structures for Riemannian homogeneous manifolds under certain extensibility assumptions on their geodesic flow is given. This is applied to generalized Heisenberg groups…
A simple integral representation is derived for the quasiclassical Green function of the Dirac equation in an arbitrary spherically-symmetric decreasing external field. The consideration is based on the use of the quasiclassical radial wave…
In this work we study differential problems in which the reflection operator and the Hilbert transform are involved. We reduce these problems to ODEs in order to solve them. Also, we describe a general method for obtaining the Green's…
Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…
Lusztig's algorithm of computing generalized Green functions of reductive groups involves an ambiguity of certain scalars. In this paper, for reductive groups of classical type with arbitrary characteristic, we determine those scalars…
We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional…
In this paper, we establish a sharp stability inequality on the Heisenberg group for functions that are close to the sum of m weakly interacting Jerison-Lee bubbles. As a consequence, we obtain a sharp quantitative stability of global…
The electroelastic 4 $\times$ 4 Green's function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form (eqs. (73) ff. and (88) ff., respectively) by using residue…
In the first part of this article we obtain an identity relating the radial spectrum of rotationally invariant geodesic balls and an isoperimetric quotient $\sum 1/\lambda_{i}^{\rm rad}=\int V(s)/S(s)ds$. We also obtain upper and lower…
Let $S$ be a closed oriented surface of genus at least $2$, and denote by $\mathcal{T}(S)$ its Teichm{\"u}ller space. For any isotopy class of closed curves $\gamma$, we compute the first three derivatives of the length function…
For the group GL(n), we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck-Springer resolution on a certain subcategory of a finite monodromic Hecke category. We use this to construct a partial…