The Paley Wiener Theorem and the Inversion of the Laplace transform скачать в хорошем качестве

The Paley Wiener Theorem and the Inversion of the Laplace transform

How do you invert the Laplace transform without a table? This is done through the Paley Wiener Theorem and Fourier transforms. We go through the proof of the Paley Wiener Theorem in this video, which tells us that when we take the inverse transform of certain analytic functions, we get an L2 signal back. This is the converse of the results that we went over in the last video. This video largely followed a PDF from Friedrich Littmann's homepage. I made a lot of modifications to get the result explicitly in terms of the Laplace transform, since the Paley Wiener theorem is most often communicated as a Fourier result. Littmann's pdf can be found here: https://www.ndsu.edu/pubweb/~littmann... //Additional Reading The Paley Wiener Theorems: https://www.ndsu.edu/pubweb/~littmann... //Exercises //Watch Next The Analyticity of the Laplace transform    • Morera's Theorem in Practice - Laplace Tra...   (The Other Pailey Wiener Theorem)    • Sampling theory and why I reject a lot of ...   Undergraduate Intro to the Laplace Transform    • MAP2302 - Definition of the Laplace Transf...   A Mature Look at the Laplace transform    • Introduction to the Laplace Transform   Introduction to Control Theory    • Introduction to Control Theory   //Music Provided by Epidemic Sound Go On - Cacti Late Nights - Daxten Mayweather - Warmkeys Late Nights - Daxten Beach Memories - Sum Wave Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel: https://www.epidemicsound.com/referra... //Books Real and Comlex Analysis - Rudin https://amzn.to/3riipvZ Real Analysis - Folland https://amzn.to/3ogVuiG Fundamentals of Differential Equations - Nagle, Saff, and Snider https://amzn.to/3qeGD9C Advanced Mathematical Analysis - Beals https://amzn.to/3fn2jdP From Vector Spaces to Function Spaces - Yutaka Yamamoto https://amzn.to/3sU2CVj Feedback Control Theory - Doyle, Francis, Tannenbaum https://amzn.to/3HFvuov Pick Interpolation and Hilbert Function Spaces - Agler and McCarthy https://amzn.to/3EOJU3K Nonlinear Systems - Khalil https://amzn.to/32Zyk8E Modern Control Systems - Dorf and Bishop https://amzn.to/331JQAm //Recording Equipment Canon SL3: https://amzn.to/3nZ11KU Canon T6i: https://amzn.to/3FUpkQh Rode VideoMic: https://amzn.to/3lhldGa Blue Yeti Microphone: https://amzn.to/3I1y88N Yeti Nano Microphone: https://amzn.to/3I1mriA SanDisc 256GB SD Card: https://amzn.to/3E3LOOr Neewer 5600K USB LED Lights: https://amzn.to/3xvB9cN Neewer 18 inch Ring Light: https://amzn.to/2ZvgCsc Camera Power Adapter: https://amzn.to/3D3upUu DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you! 0:00 Start 0:56 Where does this signal come from? 3:56 Cauchy's Theorem and Big Rectangles 6:20 FUBINATE! 8:17 What is this L2 Signal? 11:12 What's Next?