Fourier method for Laplace transform inversion.
Fourier-Laplace transforms and the Bergman spaces on tube domains
Fractional Calculus of P-transforms
MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in reaction rate...
Fractional derivative of the multivariable polynomials.
General Dirichlet series, arithmetic convolution equations and Laplace transforms
In the earlier paper [Proc. Amer. Math. Soc. 135 (2007)], we studied solutions g: ℕ → ℂ to convolution equations of the form , where are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form (), where is an additive subsemigroup. If X is discrete and a certain solvability criterion is satisfied,...
General representability problem for the Laplace transform of exponentially bounded vector-valued functions
Generalizations of the Riemann-Lebesgue and Cantor-Lebesgue lemmas
Generalized Laplace transform with matrix variables.
Global behavior of integral transforms.
Heat transfer between a fluid and a plate: multidimensional Laplace transformation methods.
Homogeneous cones and Abelian theorems.
Integrated version of the Post-Widder inversion formula for Laplace transforms
We establish an inversion formula of Post-Widder type for -multiplied vector-valued Laplace transforms (α > 0). This result implies an inversion theorem for resolvents of generators of α-times integrated families (semigroups and cosine functions) which, in particular, provides a unified proof of previously known inversion formulae for α-times integrated semigroups.
Inverse problems for memory kernels by Laplace transform methods.
Inversion of the Laplace transform from the real axis using an adaptive iterative method.
Kriterien für die Darstellbarkeit von Funktionen als verallgemeinerte Laplace-Integrale.
Kvaziasimptotičeskoe razloženie meri (Quasiasymptotic decomposition of measures).
Laguerre polynomials in the inversion of Mellin transform
In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function is represented as an expansion of Laguerre polynomials with respect to the variable . The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last...
Laplace Adomian decomposition method for solving a fish farm model
In this work, a combined form of the Laplace transform method and the Adomian decomposition method is implemented to give an approximate solution of nonlinear systems of differential equations such as fish farm model with three components nutrient, fish and mussel. The technique is described and illustrated with a numerical example.
Laplace -transform of distributions
Laplace transform generation theorems and local Cauchy problems.