منابع مشابه
The Laplace transform in control theory
The Laplace transform plays a important role in control theory. It appears in the description of linear time invariant systems, where it changes convolution operators into multiplication operators and allows to define the transfer function of a system. The properties of systems can be then translated into properties of the transfer function. In particular, causality implies that the transfer fu...
متن کاملLaplace 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...
متن کاملthe Laplace transform.
The spherical phylon group and invariants of the Laplace transform. Abstract We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of R d that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.
متن کاملInversion of the Laplace transform
Let J% exp(-PQf(t) dt = F(P) P > 0 where b > 0 is a given number. We give a formula for f (t) in terms of F (p) , p > 0. The object of this Letter is to give a formula for the inverse Laplace transform in which the data used are given on the semi-axis p > 0 only. Let P>O where b > 0 is a fixed number. We have (1, formula 4.14.1) where Jo is a Bessel function. It follows from (1) and (2) that s,...
متن کاملThe non-Archimedian Laplace Transform
Topological properties of the spaces of analytic test functions and distributions are investigated in the framework of the general theory of nonarchimedean locally convex spaces. The Laplace transform, topological isomorphism, is introduced and applied to the differential equations of nonarchimedean mathematical physics (Klein-Gordon and Dirac propagators).
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1997
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-38-1-325-338