Related papers: Boolean Differential Operators
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference theorems, one in amalgam spaces and the other in Wiener amalgam…
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
We consider an operator-differential expression of the form $$ \ell y=\frac{d^m}{dx^m}\Big(By^{(n)}+Cy\Big), \quad 0<x<1, $$ where $B$ is a linear bounded invertible operator, while $C$ is some finite-dimensional linear operator relatively…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.
A differential operator of weight $\lambda$ is the algebraic abstraction of the difference quotient $d_\lambda(f)(x):=\big(f(x+\lambda)-f(x)\big)/\lambda$, including both the derivation as $\lambda$ approaches to $0$ and the difference…
We use the definition of differential operators on noncommutative rings given by V.Lunts and A.Rosenberg to find the differential operators on Azumaya algebras and the Heisenberg algebras.
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained…
In this paper, we demonstrate an elementary method for constructing new solutions to Bochner's problem for matrix differential operators from known solutions. We then describe a large family of solutions to Bochner's problem, obtained from…
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…
It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than…
Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra $\mathbf{k}[x]$ plays a central role both in analysis…
We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators $\mathscr{D}_{q}$ and $\Delta$ and, as a limit case, the derivative operator. The objective…
We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the…
We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $so^*(12)$. We give the main multiplets of indecomposable elementary representations. Due…