Related papers: Infinite Order Differential Operators in Spaces of…
We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$…
We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the…
In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many…
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
In the enduring, fruitful research on spectral differential equations with polynomial eigenfunctions, Koornwinder's generalized Laguerre polynomials are playing a prominent role. Being orthogonal on the positive half-line with respect to…
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and show their application to the equivalence problem of such…
We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L^p-spaces over B, 1 < p < \infty. Under suitable ellipticity…
The aim of this paper is to prove continuity results for the volume potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces of negative exponent and to…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for…
We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$…
We study directional differentiability properties of solution operators of rate-independent evolution variational inequalities with full-dimensional convex polyhedral admissible sets. It is shown that, if the space of continuous functions…
We consider fourth order ordinary differential operators with compactly supported coefficients on the half-line and on the line. The Fredholm determinant for this operator is an analytic function in the whole complex plane without zero. We…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
We study the change of quantization for a class of global pseudodifferential operators of infinite order in the setting of ultradifferentiable functions of Beurling type. The composition of different quantizations as well as the transpose…
In this paper, we develop a functional analytical theory for establishing that mild solutions of first-order Cauchy problems involving homogeneous operators of order zero are strong solutions; in particular, the first-order time derivative…
We determine necessary and sufficient conditions on the ring of differential operators of a finite purely inseparable field extension of positive characteristic for determining whether the extension is modular.
We investigate the structure of norm-preserving and linear but not necessarily surjective operators on variable-exponent, discrete Lebesgue spaces. A certain class of isometries, novel to this work, are especially considered; this class…