Related papers: On differential operators and linear differential …
We revisit miscellaneous linear differential operators mostly associated with lattice Green functions in arbitrary dimensions, but also Calabi-Yau operators and order-seven operators corresponding to exceptional differential Galois groups.…
We show that analytic pseudodifferential and Fourier integral operators behave well for ultradifferentiable classes satisfying minimal regularity properties. As an application we investigate the ultradifferentiable regularity properties of…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
By means of a truncation condition on the parameters, the elliptic Ruijsenaars difference operators are restricted onto a finite lattice of points encoded by bounded partitions. A corresponding orthogonal basis of joint eigenfunctions is…
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…
A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a…
In terms of layer potential methods, this paper is devoted to study the $L^2$ boundary value problems for nonhomogeneous elliptic operators with rapidly oscillating coefficients in a periodic setting. Under a low regularity assumption on…
We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing the thin infinite elastic rod with material coefficients which periodically highly oscillate…
We develop a Fredholm alternative for a fractional elliptic operator~$\mathcal{L}$ of mixed order built on the notion of fractional gradient. This operator constitutes the nonlocal extension of the classical second order elliptic operators…
We compute temperate fundamental solutions of homogeneous differential operators with real-principal type symbols. Via analytic continuation of meromorphic distributions, fundamental solutions for these non-elliptic operators can be…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
In this work, we prove that linear bounded operators $T$ on a Banach space $X$ allowing spectral cuts along rectifiable Jordan curves meeting their spectrum are related to classes of operators admitting an unconventional functional…
We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we…
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve…
We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…
We prove the existence of minimizers for functionals defined over the class of convex domains contained inside a bounded set D of R^N and with prescribed volume. Some applications are given, in particular we prove that the eigenvalues of…
We propose an operator preconditioner for general elliptic pseudodifferential equations in a domain $\Omega$, where $\Omega$ is either in $\mathbb{R}^n$ or in a Riemannian manifold. For linear systems of equations arising from low-order…
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…
We present a Lohner type algorithm for the computation of rigorous bounds for solutions of ordinary differential equations and its derivatives with respect to initial conditions up to arbitrary order. As an application we prove the…