Related papers: Differential operators on Schwartz distributions. …
We construct explicit differential operators on hermitian modular forms, extending methods developed for Siegel modular forms. These differential operators are closely related to the two-variable spherical pluriharmonic polynomials. We…
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…
We study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we…
We define a new notion of fiber-wise linear differential operator on the total space of a vector bundle $E$. Our main result is that fiber-wise linear differential operators on $E$ are equivalent to (polynomial) derivations of an…
Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…
We compute arithmetic support of the formal deformations $D=P+tQ_1+t^2Q_2+...$ of the differential operator $P=(x\partial_x-r_1)...(x\partial_x-r_k)$, where $r_1,...,r_k\in\mathbb{Q}$ for sufficiently large primes $p$ in terms of the…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We…
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schr\"odinger operators. It provides more details and suitable extensions to already existing results, that are needed in other…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators `acting on sections of the projective bundle' in a formal…
The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most…
We define the concept of completely regular ordinary differential operators and give various criteria for operators to belong to this class. We give also criteria for Birkhof regularity of ordinary differential operators in terms of the…
We give a survey of recent work on the construction of differential operators on various types of modular forms (mod p). We also discuss a framework for determining the effect of such operators on the mod p Galois representations attached…
Fractional order derivatives and integrals (differintegrals) are viewed from a frequency-domain perspective using the formalism of Riesz, providing a computational tool as well as a way to interpret the operations in the frequency domain.…
We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra ($q$-analogue…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$,…
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the…
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…