@dmm@mathstodon.xyz avatar

dmm

@dmm@mathstodon.xyz

Retired husband/father/grandfather living in the US. Interests include #science, #math, #evolution, #machinelearning, #physics, #finance, #markets, #climatechange, #biology, #surfing, #music, and our #oceans.

B.Sc. in Biology, M.Sc. in Computer Science.

Former Director, Advanced Network Technology Center at the University of Oregon.

Former Chief Scientist, VP and Fellow at Brocade Communications Systems.

Former Senior Scientist at Sprint.

Former Distinguished Engineer at Cisco Systems.

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dmm, to math
@dmm@mathstodon.xyz avatar

Here I tried to prove the Existence Theorem for Laplace Transforms. I don't know what the/a "conventional proof" looks like, but this is what I came up with.

A few of my notes on this and related topics are here: https://davidmeyer.github.io/qc/dirac_delta.pdf

As always, questions/comments/corrections/* greatly appreciated.

dmm,
@dmm@mathstodon.xyz avatar

@johncarlosbaez BTW, thank you for all of your thoughtful comments. I really appreciate it and have learned a lot in the process. --dmm

dmm, (edited )
@dmm@mathstodon.xyz avatar

@johncarlosbaez Thanks. I came to that conclusion as well. I need to take a different approach to the proof to emphasize that showing that the integral

[M \int\limits_{0}^{\infty}e^{(c-s)t}dt ]
converges means that the Laplace transform exists..

Thanks again for connecting the dots...

dmm,
@dmm@mathstodon.xyz avatar

@johncarlosbaez Not stressful, other than I worry I'm making you work to much.

I'm just learning all of this (learning things is what I like to do), so I appreciate not only your patience but also your time.

Thanks! --dmm

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