Topologies for Laplace transform spaces

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...

On Topologies for Function Spaces

Given topological spaces Xt ÜT, and F and a function h from XXT to F which is continuous in x for each fixed ty there is associated with h a function h* from I t o F = F x , the space whose elements are the continuous functions from X to F. The function h* is defined as follows: h*(t)=ht, where ht(x)~h(x} t) for every x in X. The correspondence between h and h* is obviously one-to-one. Although...

Topologies for Probabilistic Metric Spaces

the 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.

On Generalized Injective Spaces in Generalized Topologies

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...