Related papers: Analytic Functions of a General Matrix Variable
In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…
Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential…
A non-commutative differential calculus on the $h$-superplane is presented via a contraction of the $q$-superplane. An R-matrix which satisfies both ungraded and graded Yang-Baxter equations is obtained and a new deformation of the $(1+1)$…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q-differential algebra. We study the first and higher order noncommutative differential calculus of…
One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
We introduce a more general discrete fractional operator, given by convex linear combination of the delta and nabla fractional sums. Fundamental properties of the new fractional operator are proved. As particular cases, results on delta and…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differential equations and n-ary algebras. Results on quadratic…
Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric…
The article considers arrowhead and diagonal-plus-rank-one matrices in F^(nxn) where F in R,C or H. H is a non-commutative field of quaternions. We give unified formulas for fast matrix-vector multiplications, determinants, and inverses for…
A generalized quantum distribution function is introduced. The corresponding ordering rule for non-commuting operators is given in terms of a single parameter. The origin of this parameter is in the extended canonical transformations that…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on $\mathbb{R}^d$ that are convex with respect to the L\"{o}wner partial order can have a complicated structure and might be very difficult to compute…