An Introduction to Tempered Distributions
Автор: ThatMathThing
Загружено: 2020-09-06
Просмотров: 2668
Here we define Tempered Distributions. These objects are necessary on our route to the Fourier Transform. These will ultimately allow us to talk about Fourier Transforms of periodic functions, but also will serve as prototypes of dual spaces which will come back as we approach the end of the course.
Music:
Flames by Dan Henig
Flowers in Heaven by Craig Hardgrove
Empire Seasons by Dan Henig
Chomber by Craig Hardgrove
Guardians + Tek by Craig Hardgrove
0:00 Start
9:58 Whiteboard Start - Definition of Tempered Distributions
16:23 Lemma Discussing the Continuity of Tempered Distributions
18:59 Delta Function Definition (Important)
22:17 Regular Distributions
27:52 A function is determined by its regular distribution
32:30 Example of a Non-regular Distribution
34:59 Principle Value Distribution
42:28 Abuse of Notation
46:44 Operations on Distributions (Multiplication of a distribution by a function)
52:18 Example with the delta function
55:24 Closing Remarks
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