Related papers: Dunkl derivative from moment differentiation
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
As applications of Kadison's Pythageorean and carpenter's theorems, the Schur-Horn theorem, and Thompson's theorem, we obtain an extension of Thompsons theorem to compact operators and use these ideas to give a characterization of diagonals…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…
This note is devoted to the intertwining operator in the one--dimensional trigonometric Dunkl setting. We obtain a simple integral expression of this operator and deduce its positivity.
The coefficients occurring in summation formulae of the Lubbock type are shown to be generalised Bernoulli polynomials which turn up in subdivision questions such as quantum field theory around a conical singularity and on spherical lunes.…
We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those…
Dunkl operators are differential-difference operators on $\b R^N$ which generalize partial derivatives. They lead to generalizations of Laplace operators, Fourier transforms, heat semigroups, Hermite polynomials, and so on. In this paper we…
We consider various homological operations on homology of quandles. We introduce the notion of quandle partial derivatives, and extreme chains on which appropriate partial derivatives vanish. Extreme chains yield homological operations. We…
We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the…
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange interactions defining the unitary update…
We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value…
Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
In this paper, we introduce a new differential-difference operator $T_\xi$ $(\xi \in \mathbb{R}^N)$ by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…