相关论文: Real Commuting Differential Operators Connected wi…
We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…
We consider the normal operator of the X-ray transform, weighted with Gaussian weights, in Euclidean space with dimension at least 3. We show the eigenfunctions of the normal operator are joint eigenfunctions of the harmonic oscillator and…
We study quotients of principally polarized abelian varieties with real multiplication by Galois-stable finite subgroups and describe when these quotients are principally polarizable. We use this characterization to provide an algorithm to…
We construct a commutative algebra A_z, generated by d algebraically independent q-difference operators acting on variables z_1, z_2,..., z_d, which is diagonalized by the multivariable Askey-Wilson polynomials P_n(z) considered by Gasper…
Let $D^{III}_n$ and $\mathscr{S}_n$ be the Cartan domains of type III that consist of the symmetric $n \times n$ complex matrices $Z$ that satisfy $Z\overline{Z} < I_n$ and $\mathrm{Im}(Z) > 0$, respectively. For these domains, we study…
The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, with respect to a weight W, that are eigenfunctions of a second order differential operator D. The weight W and…
We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras…
We consider one-point commuting difference operators of rank one. The coefficients of these operators depend on a functional parameter, shift operators being included only with positive degrees. We study these operators in the case of…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…
A closed symmetric differential of the 1st kind is a differential that locally is the product of closed holomorphic 1-forms. We show that closed symmetric 2-differentials of the 1st kind on a projective manifold $X$ come from maps of $X$ to…
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…
We introduce a class of bipartite operators acting on $\mathcal{H} \otimes \mathcal{H}$ ($\mathcal{H}$ being an $n$-dimensional Hilbert space) defined by a set of $n$ Completely Different Permutations CDP. Bipartite operators are of…
We study translation preserving operators, that is operators commuting with translations by a closed subgroup of a locally compact abelian group. We show that there is a one to one correspondence between these operators and range operators.…
We present a matrix version of a known method of constructing common eigenvectors of two diagonalizable commuting matrices, thus enabling their simultaneous diagonalization. The matrices may have simple eigenvalues of multiplicity greater…
In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…
We characterize matrix-valued asymmetric truncated Toeplitz operators (which are compressions of multiplication operators acting between two possibly different model spaces) by using compressed shifts, modified compressed shifts and shift…
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck's notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are…
We characterize possible periodic subvarieties for surjective endomorphisms of complex abelian varieties in terms of the eigenvalues of the cohomological actions induced by the endomorphisms, extending previous work in this direction by…
A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.