Related papers: Green's functions for magnetic Dirac operators and…
We derive the Green's functions (concentrated force and couple in an infinite space) for the isotropic planar relaxed micromorphic model. Since the relaxed micromorphic model particularises into the microstretch, Cosserat (micropolar),…
An explicit form of the magnetic moment tensor operator for non-Dirac particles with rest spin 1/2 and its essential difference from the spin operator are established. Possible consequences of the last fact for the description of the spin…
The main objective of the work is to provide sharp two-sided estimates of $\lambda$-Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtained by K. Bogus and J. Malecki [3], regarding precise…
We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions…
The complete renormalization of the generating functional for Green functions of quark currents between one-nucleon states in two flavor heavy baryon chiral perturbation theory is performed to order $q^4$. We show how the heat kernel method…
A resistance network is a connected graph $(G,c)$. The conductance function $c_{xy}$ weights the edges, which are then interpreted as resistors of possibly varying strengths. The relationship between the natural Dirichlet form $\mathcal E$…
In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system…
We study the Dirac equation of a charged massless spinor on the general charged AdS black hole of conformal gravity. The equation can be solved exactly in terms of Heun's functions. We obtain the exact Green's function in the phase space…
It is known that the equation $x'(t)=Ax(t)+f(t)$, where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~$f$ if and only if the spectrum of the coefficient $A$ does not intersect the…
We consider the 1D massless Dirac operator on the real line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following…
A problem related to some Green functions found by Guimar\~aes and Linet in the manifold of a straight cosmic string continued in the Rindler space is investigated.
The structure of diagonal singularities of Green functions of partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian man ifold is studied. A special class of operators formed by the…
Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the…
In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unimodal L\'evy processes. Our bounds are sharp under the…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior…
An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results…
Volkov states and Volkov propagator are the basic analytical tools to investigate QED processes occurring in the presence of an intense plane-wave electromagnetic field. In the present paper we provide alternative and relatively simple…
An algebraic method of constructing the confluent Natanzon potentials endowed with position-dependent mass is presented. This is possible by identifying the scaling resolvent operator (Green's function) to nonrelativistic position-dependent…