Related papers: A Brief Comment on Post inversion formula for the …
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of…
We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.
New simple proofs are given to some elementary approximate and explicit inversion formulas for Riesz potentials. The results are applied to reconstruction of functions from their integrals over Euclidean planes in integral geometry.
Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.
This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations can be mapped into Lie systems through certain Legendre…
This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging,…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…
A discrete Laplace transform and its inversion formula are obtained by using a quadrature of the continuous Fourier transform which is given in terms of Hermite polynomials and its zeros. This approach yields a convergent discrete formula…
In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some properties of the degenerate Laplace transform and degenerate gamma function. From our investigation, we derive some interesting…
In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula…
Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the…
An attempt has been made to find a consistent and logical form for relativistic temperature transformation. Other works in this area have been discussed. Our approach is based on the kinetic theory of ideal gases.
In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.
The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consider Laplace transforms of bounded functions. Our Tauberian…
The LIT approach is reviewed both for inclusive and exclusive reactions. It is shown that the method reduces a continuum state problem to a bound-state-like problem, which then can be solved with typical bound-state techniques. The LIT…
We determine an explicit formula for the Laplace transform of the price of an option on a maximal interest rate when the instantaneous rate satisfies Cox-Ingersoll-Ross's model. This generalizes considerably one result of Leblanc-Scaillet.
This article is concerned with the joint law of an integrated Wishart bridge process and the trace of an integrated inverse Wishart bridge process over the interval $ \left[0,t\right] $. Its Laplace transform is obtained by studying the…
This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the…
We provide a simple approach for the evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind the method is to reduce the inverse transform to the solution of an ordinary…
The distribution of prime numbers is here considered. We show a formula for $li^{-1}$ and we study the $\pi(x)$ function and Riemann's hypothesis.