MHB Laplace transform of a series in time t

sarrah1
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Hi

I have a series

${f}_{1}$ , ${f}_{2}$, ... that are all a functions of a variable $t$

I am seeking a point-wise convergence. to investigate the convergence of the series I took Laplace transform. If I can find a condition on the Laplace variable $s$, can I find the condition of convergence of the series on $t$.

is it normal to investigate convergence of series via Laplace transform ?
thanks
 
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Yes, it is normal to investigate the convergence of a series via Laplace transform. The Laplace transform can be used to determine the conditions on the Laplace variable $s$ for which the series converges. This then allows us to determine the conditions on the original variable $t$ for which the series converges.
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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