Related papers: Inverse Laplace Transform for Bi-Complex Variables
In this paper we extend notions of complex C-R-calculus and complex Hermite polynomials to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case.
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We show that a compact, complex analytic space $X$ has a bimeromorphic orbifold modification that is an isomorphism over the locally trivial orbifold locus of $X$.
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
In this paper, we introduce the concept and representation of modified $\lambda$-differential Lie triple systems. Next, we define the cohomology of modified $\lambda$-differential Lie triple systems with coefficients in a suitable…
We use Cramer's formula for the inverse of a matrix and a combinatorial expression for the determinant in terms of paths of an associated digraph (which can be traced back to Coates) to give a combinatorial interpretation of M\"obius…
Given a (not necessarily regular) holonomic D-module defined on the product of two complex manifolds, we prove that the associated correspondence commutes (in some sense) with the De Rham functor. We apply this result to the study of the…
We define the Laplacian operator on finite multicomplexes and give a formula for its spectra in the case of shifted multicomplexes.
This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a…
We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns…
In this paper, by the use of Potential Theory, some representation results for multivariate functions from the Sobolev spaces in terms of the double layer potential and the fundamental solution of Laplace's equation are pointed out.…
In this paper, we systematically investigate the multidimensional $Z$-transform of functions with values in sequentially complete locally convex spaces over the field of complex numbers. We provide many structural characterizations, remarks…
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
The strong dual space of linear continuous functionals on a weighted space G of infinitely differentiable functions defined on the real line is described in terms of their Fourier-Laplace transforms.