Related papers: Green function and Poisson kernel associated to ro…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
We determine the asymptotic behavior of the Arakelov metric, the Arakelov-Green's function, and the Faltings delta-invariant for arbitrary one-parameter families of complex curves with semistable degeneration. The leading terms in 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…
We present an efficient algorithm for solving local linear systems with a boundary condition using the Green's function of a connected induced subgraph related to the system. We introduce the method of using the Dirichlet heat kernel…
We consider the numerical approximation for a class of radial Dunkl processes corresponding to arbitrary (reduced) root systems in $\mathbb{R}^{d}$. This class contains some well-known processes such as Bessel processes, Dyson's Brownian…
In this paper, we introduce the operator dependent range-separated tensor approximation of the discretized Dirac delta in $\mathbb{R}^d$. It is constructed by application of the discrete elliptic operator to the range-separated…
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced…
Concise and explicit formulas for dyadic Green's functions, representing the electric and magnetic fields due to a dipole source placed in layered media, are derived in this paper. First, the electric and magnetic fields in the spectral…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^2$. Assuming that the principal coefficients satisfy the Dini mean oscillation condition, we establish the…
In this paper, we introduce the pluricomplex Green function of the Monge-Amp\`{e}re equation for $(n-1)$-plurisubharmonic functions by solving the Dirichlet problem for the form type Monge-Amp\`{e}re and Hessian equations on a punctured…
This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…
We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in $R^{n}$ indexed by a small parameter $\epsilon$. The domains depend on $\epsilon$ only within a ball of radius proportional to $\epsilon$ and,…
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
Let $(X_t)_{t\geq0}$ be the $n$-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space $\D^n$ having the Laplace-Beltrami operator as its generator. The aim of the paper is to derive the formulas for the…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We obtain the two-point Green's function for the relativistic Dirac-Oscillator problem. This is accomplished by setting up the relativistic problem in such a way that makes comparison with the nonrelativistic problem highly transparent and…
This survey synthesizes the current state of the art on the regularity theory for solutions to the optimal partition problem. Namely, we consider non-negative, vector-valued Sobolev functions whose components have mutually disjoint support,…
We establish pointwise estimates for the Green function to the Dirichlet problem for parabolic equation with coefficients measurable in time variable. Using these estimate we obtain coercive estimates for this problem in anisotropic…
We calculate the Green function for the Dirac equation describing a spin 1/2 particle in the presence of a potential which is a sum of the Coulomb potential V_C=-A_1/r and a Lorentz scalar potential V_S=-A_2/r. The bound state spectrum is…