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We present a simple inductive proof of the Lagrange Inversion Formula.

The following two inversion methods for Radon-like transforms are widely used in integral geometry and related harmonic analysis. The first method invokes mean value operators in accordance with the classical Funk-Radon-Helgason scheme. The…

We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the…

The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…

An integration by parts formula is the foundation for stochastic analysis on path spaces over a (finite dimensional) Riemannian manifold or over $R^n$, from which we may deduce the operator $d$ is closable and define the Laplacian operator…

Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the…

A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator)…

A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex…

In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…

The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively…

In this note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier \cite{BorgesZeMarcio}. As in the theory of functions of a complex variable, it is expected that…

These notes are written up after my lectures at the University of Pittsburgh in March 2014 and at Tsinghua University in May 2014. My objective is the $\infty$-Laplace Equation, a marvellous kin to the ordinary Laplace Equation. The…

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

We give a new proof for the parabolic Verlinde formula in all ranks based on a comparison of wall-crossings in Geometric Invariant Theory and certain iterated residue functionals. On the way, we develop a tautological variant of Hecke…

Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83},…

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a…

The Uehling contribution to the Lamb shift can be computed exactly in terms of the Uehling potential function. However derivations of this function are complex involving avoiding divergences using intricate techniques from early quantum…

We propose a numerical method to spline-interpolate discrete signals and then apply the integral transforms to the corresponding analytical spline functions. This represents a robust and computationally efficient technique for estimating…

This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…