Related papers: Laplacian and codifferential operators on p-forms …
In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…
This paper concerns certain $\mod p$ differential operators that act on automorphic forms over Shimura varieties of type A or C. We show that, over the ordinary locus, these operators agree with the $\mod p$ reduction of the $p$-adic theta…
Non commutative superspaces can be introduced as the Moyal-Weyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and…
We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…
Starting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an applications we find…
We discuss generalizations of Rubio de Francia's inequality for Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two versions of Rubio de Francia's operator are discussed: it is shown that a rotation factor is needed…
It has long been known that the differential operator $D$ represents a typical examples of unbounded operators in many Banach spaces including the classical Fock spaces, the Fock--Sobolev spaces, and the generalized Fock spaces where the…
We refine previous investigations on de Sitter space and extremal surfaces anchored at the future boundary $I^+$. Since such surfaces do not return, they require extra data or boundary conditions in the past (interior). In entirely…
We compute the eigenvalues with multiplicities of the Lichnerowicz Laplacian acting on the space of complex symmetric covariant tensor fields on the complex projective space $P^n(\comp)$. The spaces of symmetric eigentensors are explicitly…
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…
Recently a definition for a Lorentz invariant operator approximating the d'Alembertian in d-dimensional causal set space-times has been proposed. This operator contains several dimension-dependent constants which have been determined for…
Identities pertaining to the de Rham codifferential $\delta$ in differential geometry are scattered in the literature. This article gathers such formulas involving usual differential operators (Lie derivative, Schouten-Nijenhuis bracket,…
Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is…
We use a variational approach to study existence and regularity of solutions for a Neumann $p$-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Trace theorems…
In this paper we continue the study of compact-like operators in lattice normed spaces started recently by Aydin, Emelyanov, Erkur\c{s}un \"Ozcand and Marabeh. We show among others, that every p-compact operator between lattice normed…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
We study the deformed conformal-Poincare symmetries consistent with the Snyder--de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation…
In this note we investigate the nonelliptic differential expression A=-div sgn grad on a rectangular domain in the plane. The seemingly simple problem to associate a selfadjoint operator with the differential expression A in an L^2 setting…
We derive a manifestly duality-invariant formulation of the action principle for linearized gravity on anti de Sitter background. The analysis is based on the two-potential formalism, obtained upon resolution of the constraints in the…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…