Hardy integral estimates for the Laplace transform

Laplace Transform Using the Henstock-kurzweil Integral

We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.

Solving Fuzzy Integral Equations of the Second Kind by Fuzzy Laplace Transform Method

Integral Transforms with Exponential Kernels and Laplace Transform

Let X ←−fZ −→gY be a correspondence of complex manifolds. We study integral transforms associated to kernels exp(φ), with φ meromor-phic on Z, acting on formal or moderate cohomologies. Our main applicationis the Laplace transform. In this case, X is the projective compactification ofthe vector space V ' Cn, Y is its dual space, Z = X×Y and φ(z, w) = 〈z,w〉.We obt...

Laplace Transform Estimates and Deviation Inequalities Estimées De La Transformée De Laplace Et Inégalités De Déviation

– We derive deviation inequalities from non-asymptotic bounds of the log-Laplace transform of a function of N random variables. We assume either that these random variables are independent or that they form a Markov chain. We assume also that the partial finite differences of order one and two of the function are suitably bounded, or more generally that they have some exponential moments. The e...

Laplace Transform

We have seen before that Fourier analysis is very useful in the study of signals and linear and time invariant (LTI) systems. The main reason is that a lot of signals can be expressed as a linear combination of complex exponentials of the form e with s = jw. There are many properties that still apply when s is not restricted to be pure imaginary. That is why we introduce a generalization of the...