Related papers: Boolean Differential Operators
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 introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which…
The causal set theory d'Alembertian has rational coefficients for which alternating expressions are known. Here, a combinatorial interpretation of these numbers is given.
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
We integrate nonabelian Toda field equations for root systems of types A, B, C, for functions with values in any associative algebra. The solution is expressed via quasideterminants. In the appendix we review some results concerning…
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…
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…
We develop a spectral analysis of a class of block Jacobi operators based on the conjugate operator method of Mourre. We give several applications including scalar Jacobi operators with periodic coefficients, a class of difference operators…
A sequence $\{\delta_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
We consider the algebra of mixed multidimensional integral operators. In particular, Fredholm integral operators of the first and second kind belongs to this algebra. For the piecewise constant kernels we provide an explicit representation…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F"_4$ which is the split rank one form of the exceptional Lie algebra…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
This article explains the relationship between analytic and algebraic order in case of abstract pseudo-differential operators for a regular spectral triple.
This article provides a survey of circuit complexity bounds for basic boolean transforms exploited in digital circuit design and efficient methods for synthesizing such circuits. The exposition covers structurally simple functions and…
Based on the particular orderings introduced for the positive roots of finite dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the $osp(2r|2n)$ and $osp(2r+1|2n)$ superalgebras and the…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…