Related papers: Inverse Laplace Transform for Bi-Complex Variables
We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
In this paper we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. This theorem…
The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are…
We investigate the Wall form of unipotent elements of index two in the orthogonal group and obtain a decomposition for these elements. Also, in characteristic two, the relation between the Wall form and some invariants of the induced…
We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, xxxx (2020), in production]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum…
In this paper, we first introduce the concept and representations of modified $\lambda$-differential Lie-Yamaguti algebras. We then establish the cohomology of a modified $\lambda$-differential Lie-Yamaguti algebra with coefficients in a…
In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…
In this paper, an explicit expression is obtained for the conformally invariant higher spin Laplace operator $\mathcal{D}_{\lambda}$, which acts on functions taking values in an arbitrary (finite-dimensional) irreducible representation for…
We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…
The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular…
The author's method (math-ph/9804010) that uses the Laplace transform to find exact values for a large class of convergent series is extended to trigonometric series.
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
In this article, we introduce the notion of a double Fock space of type B. We will show that this new construction is compatible with combinatorics of counting positive and negative inversions on a hyperoctahedral group.
The leading asymptotic behaviour of the Humbert functions $\Phi_2$, $\Phi_3$, $\Xi_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly large. New integral representations of these…
A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…
We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…
We discuss a relation between bicomplexes and integrable models, and consider corresponding noncommutative (Moyal) deformations. As an example, a noncommutative version of a Toda field theory is presented.
In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…