An Introduction to Tempered Distributions скачать в хорошем качестве

An Introduction to Tempered Distributions

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